A279290 Sum of cubes of nonprime divisors of n.

1, 1, 1, 65, 1, 217, 1, 577, 730, 1001, 1, 2009, 1, 2745, 3376, 4673, 1, 6778, 1, 9065, 9262, 10649, 1, 16345, 15626, 17577, 20413, 24761, 1, 31592, 1, 37441, 35938, 39305, 42876, 55226, 1, 54873, 59320, 73577, 1, 86310, 1, 95897, 95230, 97337, 1, 131033, 117650, 141626, 132652, 158249, 1, 183925, 166376

Offset

1,4

Comments

a(n) = 1 when n = 1 or n is prime.

a(p^k) = (p^(3*k+3) - 1)/(p^3 - 1) - p^3 for p is prime.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Index entries for sequences related to sums of divisors

Formula

a(n) = A001158(n) - A005064(n).

Example

a(4) = 65 because 4 has 2 nonprime divisors {1,4} and 1^3 + 4^3 = 65.

Mathematica

Table[DivisorSum[n, #1^3 & ,  !PrimeQ[#1] & ], {n, 55}]
Table[DivisorSigma[3, n] - DivisorSum[n, #1^3 & , PrimeQ[#1] & ], {n, 55}]
Table[Total[Select[Divisors[n], !PrimeQ[#]&]^3], {n, 60}] (* Harvey P. Dale, Aug 02 2024 *)

Crossrefs

Cf. A001158, A005064, A023890, A189120.

Sequence in context: A295175 A351308 A364072 * A034061 A113696 A302210

Adjacent sequences: A279287 A279288 A279289 * A279291 A279292 A279293

Keyword

nonn,easy

Author

Ilya Gutkovskiy, Dec 12 2016

Status

approved