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

1,2

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

Mathematica

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

Prog

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

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))).

Sequence in context: A333833 A057895 A111369 * A320149 A346305 A140760

Adjacent sequences: A190500 A190501 A190502 * A190504 A190505 A190506

Keyword

nonn

Author

T. D. Noe, May 11 2011

Status

approved