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A351195
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Sum of the 7th powers of the primes dividing n.
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11
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0, 128, 2187, 128, 78125, 2315, 823543, 128, 2187, 78253, 19487171, 2315, 62748517, 823671, 80312, 128, 410338673, 2315, 893871739, 78253, 825730, 19487299, 3404825447, 2315, 78125, 62748645, 2187, 823671, 17249876309, 80440, 27512614111, 128, 19489358, 410338801
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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^7.
G.f.: Sum_{k>=1} prime(k)^7 * x^prime(k) / (1 - x^prime(k)). - Ilya Gutkovskiy, Feb 16 2022
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MATHEMATICA
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Array[DivisorSum[#, #^7 &, PrimeQ] &, 50]
f[p_, e_] := p^7; 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), A351193 (k=5), A351194 (k=6), this sequence (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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