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A050226
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Numbers m such that m divides Sum_{k = 1..m} A000005(k).
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28
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1, 4, 5, 15, 42, 44, 47, 121, 336, 340, 347, 930, 2548, 6937, 6947, 51322, 379097, 379131, 379133, 2801205, 20698345, 56264090, 56264197, 152941920, 152942012, 8350344420, 61701166395, 455913379395, 455913379831, 1239301050694, 3368769533660, 3368769533812
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OFFSET
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1,2
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REFERENCES
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Julian Havil, "Gamma: Exploring Euler's Constant", Princeton University Press, Princeton and Oxford, pp. 112-113, 2003.
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LINKS
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FORMULA
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m is in the sequence if Sum_{i = 1..m} d(i) = m*k, k an integer, where d(i) = number of divisors of i.
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EXAMPLE
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For k = 15 the sum is 1 + 2 + 2 + 3 + 2 + 4 + 2 + 4 + 3 + 4 + 2 + 6 + 2 + 4 + 4 = 45 which is divisible by 15.
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MATHEMATICA
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s = 0; Do[ s = s + DivisorSigma[ 0, n ]; If[ Mod[ s, n ] == 0, Print[ n ] ], {n, 1, 2*10^9} ]
k=10^6; a[1]=1; a[n_]:=a[n]=DivisorSigma[0, n]+a[n-1]; nd=a/@Range@k; Select[Range@k, Divisible[nd[[#]], #]&] (* Ivan N. Ianakiev, Apr 30 2016 *)
Module[{nn=400000}, Select[Thread[{Range[nn], Accumulate[DivisorSigma[0, Range[nn]]]}], Divisible[#[[2]], #[[1]]]&]][[All, 1]] (* The program generates the first 19 terms of the sequence. To generate more, increase the nn constant. *) (* Harvey P. Dale, Jul 03 2022 *)
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PROG
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(PARI) lista(nn) = {my(s = 0); for (n=1, nn, s += numdiv(n); if (!(s % n), print1(n, ", ")); ); } \\ Michel Marcus, Dec 14 2015
(Sage)
a, L = 0, []
for n in (1..len):
a += sigma(n, 0)
if n.divides(a): L.append(n)
return L
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CROSSREFS
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KEYWORD
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nonn,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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