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A345301
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a(n) = Sum_{p|n, p prime} p^pi(n/p).
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4
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0, 1, 1, 2, 1, 7, 1, 4, 9, 13, 1, 17, 1, 23, 52, 16, 1, 43, 1, 41, 130, 43, 1, 113, 125, 77, 81, 113, 1, 270, 1, 64, 364, 145, 968, 371, 1, 275, 898, 881, 1, 1328, 1, 377, 1354, 535, 1, 1241, 2401, 1137, 2476, 681, 1, 2699, 4456, 2913, 6922, 1053, 1, 10710, 1, 2079, 8962
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OFFSET
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1,4
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COMMENTS
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If p is prime, a(p) = Sum_{p|p} p^pi(p/p) = p^0 = 1.
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LINKS
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EXAMPLE
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a(12) = Sum_{p|12} p^pi(12/p) = 2^pi(6) + 3^pi(4) = 2^3 + 3^2 = 17.
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MATHEMATICA
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Table[Sum[k^PrimePi[n/k] (PrimePi[k] - PrimePi[k - 1]) (1 - Ceiling[n/k] + Floor[n/k]), {k, n}], {n, 80}]
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PROG
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(Python)
from sympy import primefactors, primepi
def A345301(n): return sum(p**primepi(n//p) for p in primefactors(n)) # Chai Wah Wu, Jun 13 2021
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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