A046839 Numbers k such that the number of divisors of k divides the sum of cubes of divisors of k.

1, 3, 5, 6, 7, 11, 13, 14, 15, 17, 19, 20, 21, 22, 23, 27, 29, 30, 31, 33, 35, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 49, 51, 53, 54, 55, 56, 57, 59, 60, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 73, 77, 78, 79, 83, 85, 86, 87, 89, 91, 92, 93, 94, 95, 96, 97, 99, 101, 102, 103

Offset

1,2

Comments

The first 42 terms agree with A003601 but a(43)=64 is not present in A003601.

Links

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

Example

a(43) = 64. The sigma(k,64) values for k=0,1,2,3 are as follows: 7, 127, 5461 and 299593. While 7 does not divide the sum of divisors, 127, it divides the sum of d^3 values: Sum(d^3) = 299593 = 7*127*337.

Mathematica

Select[Range[103], Divisible[DivisorSigma[3, #], DivisorSigma[0, #]] &] (* Jayanta Basu, Jun 29 2013 *)

Prog

(Magma) [n: n in [1..110] | IsZero(DivisorSigma(3, n) mod NumberOfDivisors(n))]; // Bruno Berselli, Apr 11 2013
(PARI) isok(n) = sigma(n, 3) % numdiv(n) == 0; \\ Michel Marcus, May 13 2018

Crossrefs

Cf. A003601, A020486.

Sequence in context: A242076 A349897 A064728 * A003601 A328557 A216782

Adjacent sequences: A046836 A046837 A046838 * A046840 A046841 A046842

Keyword

nonn

Author

Labos Elemer

Status

approved