A005069 Sum of odd primes dividing n.

0, 0, 3, 0, 5, 3, 7, 0, 3, 5, 11, 3, 13, 7, 8, 0, 17, 3, 19, 5, 10, 11, 23, 3, 5, 13, 3, 7, 29, 8, 31, 0, 14, 17, 12, 3, 37, 19, 16, 5, 41, 10, 43, 11, 8, 23, 47, 3, 7, 5, 20, 13, 53, 3, 16, 7, 22, 29, 59, 8, 61, 31, 10, 0, 18, 14, 67, 17, 26, 12, 71, 3, 73, 37, 8, 19, 18, 16, 79

Offset

1,3

Comments

Primes counted without multiplicity. - Harvey P. Dale, Aug 28 2019

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Formula

Additive with a(p^e) = 0 if p = 2, p otherwise.

G.f.: Sum_{k>=2} prime(k)*x^prime(k)/(1 - x^prime(k)). - Ilya Gutkovskiy, Dec 24 2016

From Antti Karttunen, Jul 10 & 11 2017: (Start)

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

a(n) = A008472(A000265(n)) = A008472(n) - 2*A059841(n).

a(n) = A005078(n) + A005082(n).

(End)

Mathematica

a = {0, 0}; For[n = 3, n < 80, n++, su = 0; b = FactorInteger[n]; For[i = 1, i < Length[b] + 1, i++, If[OddQ[b[[i, 1]]], su = su + b[[i, 1]]]]; AppendTo[a, su]]; a (* Stefan Steinerberger, Jun 02 2007 *)
Array[DivisorSum[#, # &, And[PrimeQ@ #, OddQ@ #] &] &, 79] (* Michael De Vlieger, Jul 11 2017 *)
Join[{0}, Table[Total[FactorInteger[n][[All, 1]]/.(2->0)], {n, 2, 100}]] (* Harvey P. Dale, Aug 28 2019 *)

Prog

(Scheme) (define (A005069 n) (cond ((= 1 n) 0) ((even? n) (A005069 (/ n 2))) (else (+ (A020639 n) (A005069 (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)); \\ Michel Marcus, Jul 11 2017

Crossrefs

Cf. A000265, A005066, A005067, A005068, A005078, A005082, A008472, A020639, A028234, A059841.

Sequence in context: A076109 A078788 A284599 * A366840 A284233 A326990

Adjacent sequences: A005066 A005067 A005068 * A005070 A005071 A005072

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Stefan Steinerberger, Jun 02 2007

Status

approved