NT_SIGMA Function (Gnumeric)

• Introduced: First release not established; present in the retained 1.12.57 source.
• Supported in: Gnumeric 1.12.62; no retirement is established.
• Scope: Desktop Gnumeric with its Number Theory plugin. English comma-separated formulas are shown.
• Checked: October 14, 2026. Tables and the named advanced check were recalculated with 1.12.57 ssconvert. Current 1.12.62 source was inspected; the later release was not executed.

NT_SIGMA adds all positive divisors of a positive integer. It includes the integer itself. For 12, 1+2+3+4+6+12=28. This is the sum-of-divisors function sigma(n), not a standard deviation or the divisor count. Versioned function help.

=NT_SIGMA(n)

n is one required numeric argument. The wrapper floors it and then enforces a positive-domain and version-specific magnitude limit. Thus 9.9 is treated as 9, whose positive divisors sum to 13. At n=1, the sum is 1.

Current implementation.

These eight native integer results were independently checked by binary arithmetic or elementary number theory.

To obtain the sum of proper positive divisors of a validated n, subtract n from NT_SIGMA(n). For 28, the complete sum is 56 and the proper-divisor sum is 28. The native check =NT_SIGMA(28)-2*28 returned 0, the perfect-number condition.

That condition differs from merely asking whether the result is even. An abundant integer has a proper-divisor sum larger than itself; for 12, 28−12=16 exceeds 12. The examples demonstrate these small integer interpretations, not a general large-number classifier.

For a prime power p^a, the divisor sum is 1+p+…+p^a. For a product of coprime prime powers, multiply those geometric sums. For 60=2²×3×5, sigma(60)=(1+2+4)(1+3)(1+5)=7×4×6=168.

A numerically innocent-looking formula can have a large intermediate value. The older source forms p^(a+1) before dividing by p−1. The current helper rearranges that step to avoid this intermediate overflow. This is why passing the small examples cannot certify an older executable for every allowed n.

For the standard binary64 build, the older shared input bound is 2^52 = 4503599627370496. The pinned 1.12.62 expression raises it to 2^53 = 9007199254740992. This change is established by comparing the older bound with the current bound; it is not a native test of 1.12.62. Input acceptance and exact representability of every resulting integer are separate questions.

The 1.12.61 release notes record the overflow fix. The current divisor-sum helper avoids the older overflowing power intermediate.

The 1.12.61 release notes explicitly record an NT_SIGMA overflow fix. The retained native results come from 1.12.57, before that fix; none of the listed small reference inputs exercises the corrected large-intermediate branch. Use the pinned current source to understand the improvement, but do not interpret it as a fresh later-version execution test. Invalid-domain and malformed-text errors remain separate.

F5 is an actually empty cell. Listed errors are native error results, not mathematical zeroes.

• Current worksheet implementation
• Tested-version worksheet implementation
• Current calculation helper
• Tested-version calculation helper

The retained workbook contained a deliberately stale SUM cache and an uncached SUM formula, both recalculated correctly. Native evidence covers the listed 1.12.57 cases. Other worksheet layouts and mathematical interpretations are separately explained checks. GUI entry, other locales and later-release output were not tested.

SUM, POWER.