A015770 Numbers k such that phi(k) divides sigma_12(k).

1, 2, 3, 6, 249, 498, 118578, 99295058, 297885174, 4005374907

Offset: 1

Author

Robert G. Wilson v

Keywords

• nonn
• more

Comments

sigma_12(n) = A013960(n) is the sum of the 12th powers of the divisors of n.

sigma(24j+12,x)/phi(x) is an integer for j in the range 0, ..., 500 for x = 1, 2, 3, 6, 249, 498, 118578 and supposed to hold for possible larger terms of A015770 and all j. Compare with comments to A015759, A091285, A015762. - Labos Elemer, May 27 2004

a(11) > 5*10^9. - Giovanni Resta, Aug 22 2017

All known terms of A015762 (and also of this sequence) are squarefree. In that case, sigma_12(x)/sigma_4(x) = Product_{primes p|x} (p^8 - p^4 + 1) is an integer, so x is also in this sequence. - M. F. Hasler, Aug 22 2017

Crossrefs

Cf. A020492, A015759, A015761, A015762, A015763, A015764, A015765, A015766, A015767, A015768, A015769, A015771, A015773, A015774, A094470.

Programs

Mathematica

Select[Range[1200000],Divisible[DivisorSigma[12,#],EulerPhi[#]]&] (* Harvey P. Dale, Dec 04 2015 *)

Extensions

Corrected by Harvey P. Dale, Dec 04 2015

Offset corrected by and a(8)-a(10) from Giovanni Resta, Aug 22 2017