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A351193
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Sum of the 5th powers of primes dividing n.
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11
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0, 32, 243, 32, 3125, 275, 16807, 32, 243, 3157, 161051, 275, 371293, 16839, 3368, 32, 1419857, 275, 2476099, 3157, 17050, 161083, 6436343, 275, 3125, 371325, 243, 16839, 20511149, 3400, 28629151, 32, 161294, 1419889, 19932, 275, 69343957, 2476131, 371536, 3157
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = Sum_{p|n, p prime} p^5.
G.f.: Sum_{k>=1} prime(k)^5 * x^prime(k) / (1 - x^prime(k)). - Ilya Gutkovskiy, Feb 16 2022
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MAPLE
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f:= n -> add(p^5, p = numtheory:-factorset(n)):
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MATHEMATICA
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Array[DivisorSum[#, #^5 &, PrimeQ] &, 50]
f[p_, e_] := p^5; a[n_] := Plus @@ f @@@ FactorInteger[n]; a[1] = 0; Array[a, 100] (* Amiram Eldar, Jun 20 2022 *)
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CROSSREFS
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Sum of the k-th powers of the primes dividing n for k=0..10 : A001221 (k=0), A008472 (k=1), A005063 (k=2), A005064 (k=3), A005065 (k=4), this sequence (k=5), A351194 (k=6), A351195 (k=7), A351196 (k=8), A351197 (k=9), A351198 (k=10).
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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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