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A333842 G.f.: Sum_{k>=1} k * x^(prime(k)^2) / (1 - x^(prime(k)^2)). 1
0, 0, 0, 1, 0, 0, 0, 1, 2, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 1, 0, 0, 0, 1, 3, 0, 2, 1, 0, 0, 0, 1, 0, 0, 0, 3, 0, 0, 0, 1, 0, 0, 0, 1, 2, 0, 0, 1, 4, 3, 0, 1, 0, 2, 0, 1, 0, 0, 0, 1, 0, 0, 2, 1, 0, 0, 0, 1, 0, 0, 0, 3, 0, 0, 3, 1, 0, 0, 0, 1, 2, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 1, 0, 0, 0, 1, 0, 4, 2, 4, 0, 0, 0, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,9
COMMENTS
Sum of indices of non-unitary prime factors of n (prime factors for which the exponent exceeds 1).
LINKS
FORMULA
a(n) = A056239(A071773(n)) = A066328(A003557(n)). - Peter Munn and Antti Karttunen, Jun 13 2020
EXAMPLE
a(450) = a(2 * 3^2 * 5^2) = a(prime(1) * prime(2)^2 * prime(3)^2) = 2 + 3 = 5.
MATHEMATICA
nmax = 104; CoefficientList[Series[Sum[k x^(Prime[k]^2)/(1 - x^(Prime[k]^2)), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
PROG
(PARI) A333842(n) = { my(f=factor(n)); sum(k=1, #f~, if(1==f[k, 2], 0, 1)*primepi(f[k, 1])); }; \\ Antti Karttunen, Jun 12 2020
CROSSREFS
Cf. A003557, A005117 (positions of 0's), A056170, A056239, A063958, A066328, A071773.
Sequence in context: A284574 A206499 A277885 * A334109 A109527 A362424
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Apr 07 2020
STATUS
approved

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Last modified March 28 04:13 EDT 2024. Contains 371235 sequences. (Running on oeis4.)