A085045 Smallest k such that tau(n + k) = tau(n*k), or 0 if no such number exists, where tau = A000005.

2, 1, 5, 2, 3, 134, 3, 4, 11, 2, 3, 548, 2, 1, 3, 2, 5, 402, 2, 316, 1, 38, 3, 1236, 3, 1, 13, 2, 5, 1986, 2, 16, 1, 1, 19, 1644, 2, 1, 13, 716, 4, 1398, 3, 1, 15, 14, 11, 2472, 3, 10, 5, 2, 2, 1146, 23, 4, 1, 14, 3, 11028, 13, 4, 3, 2, 23, 1194, 2, 2, 9, 2

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..1000

Example

a(4) = 2 as tau(4+2) = tau(6) = 4 and tau(4*2) = tau(8) = 4.

Maple

f:= proc(n) local k; for k from 1 do if NumberTheory:-tau(n+k)=NumberTheory:-tau(n*k) then return k fi od end proc:
map(f, [$1..100]); # Robert Israel, May 26 2026

Mathematica

f[n_] := Block[{k = 1}, While[ DivisorSigma[0, n + k] != DivisorSigma[0, n*k], k++ ]; k]; Table[ f[n], {n, 1, 80}]

Crossrefs

Cf. A000005, A005237 (a(n)=1), A396005.

Sequence in context: A205106 A351743 A144019 * A093664 A298212 A087620

Adjacent sequences: A085042 A085043 A085044 * A085046 A085047 A085048

Keyword

nonn

Author

Amarnath Murthy, Jun 20 2003

Extensions

Corrected and extended by Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Jun 25 2003

Offset corrected by Sean A. Irvine, May 25 2026

Status

approved