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A319194
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a(n) = Sum_{k=1..n} sigma(n,k).
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17
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1, 6, 38, 373, 4461, 68033, 1202753, 24757484, 574608039, 14925278329, 427729375161, 13424413453317, 457608305315211, 16841852554413561, 665483754539870667, 28101844918556128030, 1262901795439193700478, 60182608193322255156347, 3031285556584399354961535
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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) ~ n^n / (1 - exp(-1)).
a(n) = Sum_{k=1..n} k^n * floor(n/k). - Daniel Suteu, Nov 10 2018
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MAPLE
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with(NumberTheory): seq(sum(sigma[n](k), k = 1..n), n = 1..20); # Vaclav Kotesovec, Aug 20 2019
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MATHEMATICA
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Table[Sum[DivisorSigma[n, k], {k, 1, n}], {n, 1, 20}]
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PROG
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(PARI) a(n) = sum(k=1, n, sigma(k, n)); \\ Michel Marcus, Sep 13 2018
(PARI) a(n) = sum(k=1, n, k^n * (n\k)); \\ Daniel Suteu, Nov 10 2018
(Python)
from math import isqrt
from sympy import bernoulli
def A319914(n): return (((s:=isqrt(n))+1)*((b:=bernoulli(n+1))-bernoulli(n+1, s+1))+sum(k**n*(n+1)*((q:=n//k)+1)-b+bernoulli(n+1, q+1) for k in range(1, s+1)))//(n+1) # Chai Wah Wu, Oct 21 2023
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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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