A392364 a(n) is the least positive integer k such that tau(k)*tau(n)/(tau(k) + tau(n)) is an integer. If no such k exists a(n) = -1. tau(i) = A000005(i).

-1, 2, 2, 12, 2, 6, 2, 6, 12, 6, 2, 4, 2, 6, 6, 240, 2, 4, 2, 4, 6, 6, 2, 24, 12, 6, 6, 4, 2, 24, 2, 4, 6, 6, 6, 180, 2, 6, 6, 24, 2, 24, 2, 4, 4, 6, 2, 48, 12, 4, 6, 4, 2, 24, 6, 24, 6, 6, 2, 6, 2, 6, 4, 2880, 6, 24, 2, 4, 6, 24, 2, 6, 2, 6, 4, 4, 6, 24, 2

Offset

1,2

Links

Michel Marcus, Table of n, a(n) for n = 1..10000

Formula

For n > 1, a(A037992(n)) = n.

Example

For n = 4: tau(k)*3/(tau(k) + 3) is an integer for the least k = 12, thus a(4) = 12.

Mathematica

a[1]=-1; a[n_]:=Module[{k=1}, While[!IntegerQ[DivisorSigma[0, k]*DivisorSigma[0, n]/(DivisorSigma[0, k]+DivisorSigma[0, n])], k++]; k]; Array[a, 79] (* Stefano Spezia, Feb 21 2026 *)

Prog

(PARI) a(n) = if (n==1, -1, my(k=1); while (denominator(numdiv(k)*numdiv(n)/(numdiv(k) + numdiv(n))) != 1, k++); k); \\ Michel Marcus, Feb 21 2026

Crossrefs

Cf. A000005, A037992, A063427.

Sequence in context: A264712 A217094 A394489 * A076976 A291757 A286464

Adjacent sequences: A392361 A392362 A392363 * A392365 A392366 A392367

Keyword

sign

Author

Ctibor O. Zizka, Feb 21 2026

Status

approved