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A005066 Sum of squares of odd primes dividing n. 5
0, 0, 9, 0, 25, 9, 49, 0, 9, 25, 121, 9, 169, 49, 34, 0, 289, 9, 361, 25, 58, 121, 529, 9, 25, 169, 9, 49, 841, 34, 961, 0, 130, 289, 74, 9, 1369, 361, 178, 25, 1681, 58, 1849, 121, 34, 529, 2209, 9, 49, 25, 298, 169, 2809, 9, 146, 49, 370, 841, 3481, 34, 3721, 961, 58, 0, 194, 130, 4489, 289, 538, 74, 5041, 9, 5329, 1369 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

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

FORMULA

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

G.f.: Sum_{k>=2} prime(k)^2*x^prime(k)/(1 - x^prime(k)). - Ilya Gutkovskiy, Jan 04 2017

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)^2 + a(A028234(n)).

a(n) = A005063(A000265(n)).

a(n) = A005079(n) + A005083(n).

(End)

MATHEMATICA

Table[Total[Select[Divisors[n], OddQ[#]&&PrimeQ[#]&]^2], {n, 60}] (* Harvey P. Dale, May 02 2012 *)

Array[DivisorSum[#, #^2 &, And[PrimeQ@ #, OddQ@ #] &] &, 74] (* Michael De Vlieger, Jul 11 2017 *)

PROG

(PARI) a(n) = sumdiv(n, d, ((d%2) && isprime(d))*d^2); \\ Michel Marcus, Jan 04 2017

(Scheme) (define (A005066 n) (cond ((= 1 n) 0) ((even? n) (A005066 (/ n 2))) (else (+ (A000290 (A020639 n)) (A005066 (A028234 n)))))) ;; Antti Karttunen, Jul 10 2017

(Python)

from sympy import primefactors

def a(n): return sum(p**2 for p in primefactors(n) if p % 2)

print([a(n) for n in range(1, 101)]) # Indranil Ghosh, Jul 11 2017

CROSSREFS

Cf. A000265, A000290, A005063, A005067, A005068, A005069, A005079, A005083, A020639, A028234.

Sequence in context: A067153 A057405 A167354 * A076262 A167301 A177741

Adjacent sequences:  A005063 A005064 A005065 * A005067 A005068 A005069

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Antti Karttunen, Jul 10 2017

STATUS

approved

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Last modified May 14 19:53 EDT 2021. Contains 343903 sequences. (Running on oeis4.)