A141059 Number of numbers m such that n = 0 (mod usigma(m)), where usigma(m) is the sum of unitary divisors of m (A034448).

1, 1, 2, 2, 2, 3, 1, 3, 3, 3, 1, 6, 1, 2, 3, 3, 2, 6, 1, 6, 2, 1, 1, 10, 2, 2, 3, 4, 1, 8, 1, 5, 3, 2, 2, 11, 1, 2, 2, 8, 1, 6, 1, 3, 4, 1, 1, 13, 1, 5, 3, 3, 1, 9, 2, 6, 2, 1, 1, 17, 1, 2, 3, 5, 3, 4, 1, 5, 2, 5, 1, 21, 1, 2, 3, 3, 1, 5, 1, 11, 3, 2, 1, 13, 3, 1, 2, 4, 1, 15, 1, 2, 2, 1, 2, 19, 1, 3, 4, 9, 1, 6

Offset: 1

Author

Yasutoshi Kohmoto, Aug 01 2008

Keywords

• nonn

Comments

If p is prime but not a Fermat prime then a(p)=1.

Least k such that a(k) = n: 1, 3, 6, 28, 32, 12, 112, 30, 54, 24, 36, 126, 48, 200, 90, 160, 60, 264, 96, 400, ..., . - Robert G. Wilson v, Aug 07 2008

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A034448, A063974.

Programs

Mathematica

usigma[n_] := Block[{d = Divisors[n]}, Plus @@ Select[d, GCD[ #, n/# ] == 1 &]]; f[n_] := Block[{c = 0, m = 1}, While[m <= n, If[ Mod[n, usigma@ m] == 0, c++ ]; m++ ]; c]; Array[f, 102] (* Robert G. Wilson v, Aug 07 2008 *)

Extensions

More terms from Robert G. Wilson v, Aug 07 2008