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A005067 Sum of cubes of odd primes dividing n. 5
0, 0, 27, 0, 125, 27, 343, 0, 27, 125, 1331, 27, 2197, 343, 152, 0, 4913, 27, 6859, 125, 370, 1331, 12167, 27, 125, 2197, 27, 343, 24389, 152, 29791, 0, 1358, 4913, 468, 27, 50653, 6859, 2224, 125, 68921, 370, 79507, 1331, 152, 12167, 103823, 27, 343, 125, 4940, 2197, 148877, 27, 1456, 343, 6886, 24389, 205379, 152 (list; graph; refs; listen; history; text; internal format)
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)

a(1) = 0; after which, for even n: a(n) = a(n/2), for odd n: a(n) = A020639(n)^3 + a(A028234(n)).

a(n) = A005064(A000265(n)).

(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

Cf. A000265, A000578, A005064, A005066, A005068, A005069, A020639, A028234, A065091.

Sequence in context: A277042 A224118 A178737 * A163574 A076108 A040735

Adjacent sequences:  A005064 A005065 A005066 * A005068 A005069 A005070

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Antti Karttunen, Jul 10 2017

STATUS

approved

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Last modified September 25 20:01 EDT 2020. Contains 337344 sequences. (Running on oeis4.)