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A005069
Sum of odd primes dividing n.
11
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
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
KEYWORD
nonn,easy
EXTENSIONS
More terms from Stefan Steinerberger, Jun 02 2007
STATUS
approved