OFFSET
1,3
LINKS
Harvey P. Dale (terms 1 .. 1000) & Antti Karttunen, Table of n, a(n) for n = 1..10000
FORMULA
Additive with a(p^e) = 0 if p = 2, p^3 otherwise.
G.f.: Sum_{k>=2} prime(k)^3*x^prime(k)/(1 - x^prime(k)). - Ilya Gutkovskiy, Jan 06 2017
From Antti Karttunen, Jul 10 2017: (Start)
(End)
MATHEMATICA
Join[{0}, Table[Total[Select[Transpose[FactorInteger[n]][[1]], OddQ]^3], {n, 2, 50}]] (* Harvey P. Dale, Jun 09 2016 *)
Array[DivisorSum[#, #^3 &, And[PrimeQ@ #, OddQ@ #] &] &, 60] (* Michael De Vlieger, Jul 11 2017 *)
PROG
(Scheme) (define (A005067 n) (cond ((= 1 n) 0) ((even? n) (A005067 (/ n 2))) (else (+ (A000578 (A020639 n)) (A005067 (A028234 n)))))) ;; Antti Karttunen, Jul 10 2017
(PARI) a(n) = my(f=factor(n)); sum(k=1, #f~, if (((p=f[k, 1])%2) == 1, p^3)); \\ Michel Marcus, Jul 11 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Antti Karttunen, Jul 10 2017
STATUS
approved