A190503 Numbers k such that sigma(phi(k)) divides sigma(k).

1, 2, 6, 12, 14, 22, 24, 28, 44, 46, 48, 56, 68, 87, 88, 92, 94, 96, 112, 118, 166, 174, 176, 184, 188, 192, 214, 224, 236, 332, 334, 352, 358, 362, 368, 376, 384, 390, 410, 428, 448, 454, 472, 526, 664, 668, 694, 704, 716, 718, 736, 752, 766, 768, 856, 896

Offset: 1

Author

T. D. Noe, May 11 2011

Keywords

• nonn

Comments

These numbers appear indirectly in A067740, which seeks the least k such that sigma(k)/sigma(phi(k)) = n. Most of these numbers are even. The odd terms (1, 87, 1257, 41559, 56679, ...) all appear to produce sigma(k)/sigma(phi(k)) = 1.

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000010 (phi), A000203 (sigma), A062402, A067740.

Cf. A033631 (k such that sigma(k)/sigma(phi(k)) = 1).

Cf. A066831 (k such that sigma(k) divides sigma(phi(k))).

Programs

Mathematica

Select[Range[1000], IntegerQ[DivisorSigma[1,#]/DivisorSigma[1,EulerPhi[#]]] &]

PARI

is(k) = {my(f = factor(k), s = sigma(f), p = eulerphi(f)); !(s % sigma(p));} \\ Amiram Eldar, May 17 2024