A015765 Numbers n such that phi(n) | sigma_7(n).

1, 2, 3, 6, 12, 14, 15, 30, 35, 42, 56, 70, 78, 105, 140, 168, 190, 210, 248, 264, 270, 295, 357, 418, 420, 570, 590, 594, 616, 630, 714, 744, 767, 812, 840, 885, 910, 1038, 1045, 1240, 1254, 1416, 1485, 1534, 1589, 1672, 1770, 1848, 2065, 2090, 2214, 2301, 2376, 2422, 2436, 2580, 2730, 2970

Offset: 1

Author

Robert G. Wilson v

Keywords

• nonn
• easy

Comments

sigma_7(n) is the sum of the 7th powers of the divisors of n.

In contrast to other values of k for which sigma_k(n) is much less frequently divisible by phi(n) (cf. A015762 (k=4: a(7) > 10^11 if it exists), A015759 (k=2: a(23) > 10^11)), it is quite easy to compute hundreds or even thousands of terms of the present sequence. - M. F. Hasler, Aug 26 2017

Links

• M. F. Hasler, Table of n, a(n) for n = 1..10000 (first 1001 terms from Vincenzo Librandi)

Programs

Mathematica

Select[Range[2100],Divisible[DivisorSigma[7,#],EulerPhi[#]]&] (* Harvey P. Dale, Aug 17 2013 *)

PARI

select( is(n)=sigma(n,7)%eulerphi(n)==0, [1..3000]) \\ M. F. Hasler, Aug 26 2017

Extensions

Third line of data completed by M. F. Hasler, Aug 26 2017