A046841 Numbers whose sum of divisors divides their sum of cubes of divisors.

1, 2, 3, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 24, 26, 27, 29, 30, 31, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 46, 47, 48, 51, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85

Offset: 1

Author

Labos Elemer

Keywords

• nonn

Comments

A005117 (squarefree numbers) is a subsequence. - Ivan Neretin, Dec 20 2017

Examples

			2 is a term because 1 + 8 = 9 is divisible by 1 + 2 = 3.
208 is a term: The power sums of divisors for k = 0, 1, 2, 3 are as follows: 10, 434, 54970, 10288838, and sigma(1,208) = 434 divides sigma(3,208) = 10288838 = 434*23707.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Paolo P. Lava)

Crossrefs

Cf. A000203, A001158, A005117.

Cf. A003601, A020486.

Programs

Maple

with(numtheory):
for n to 100 do
 if (type(sigma[3](n)/sigma[1](n), integer)) then print(n) end if;
end do; # Peter Bala, Jan 12 2025

Mathematica

Select[Range@ 85, Divisible[DivisorSigma[3, #], DivisorSigma[1, #]] &] (* Michael De Vlieger, Aug 01 2017 *)

PARI

isA046841(n)=sigma(n,3)%sigma(n,1)==0 \\ Michael B. Porter, Apr 07 2010