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A050226
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Numbers n such that n divides Sum_{k = 1..n} A000005(k).
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17
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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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listen;
history;
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internal format)
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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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Donovan Johnson, Table of n, a(n) for n = 1..39 (quotients <= 40)
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FORMULA
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n is in the sequence if Sum_{i = 1..n} d(i) = n*k, k an integer, where d(n) = number of divisors of n.
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EXAMPLE
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For n = 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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MAPLE
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with(numtheory); ListA050226:=proc(q) local a, n; a:=0;
for n from 1 to q do a:=a+tau(n); if (a mod n)=0 then print(n); fi;
od; end: ListA050226(10^9); # Paolo P. Lava, Jun 28 2013
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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 *)
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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)
def A050226_list(len):
a, L = 0, []
for n in (1..len):
a += sigma(n, 0)
if n.divides(a): L.append(n)
return L
A050226_list(10000) # Peter Luschny, Dec 18 2015
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CROSSREFS
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Cf. A000005, A006218, A057494, A085567, A085829.
Sequence in context: A006491 A304921 A051721 * A119562 A289021 A323627
Adjacent sequences: A050223 A050224 A050225 * A050227 A050228 A050229
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KEYWORD
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nonn,nice
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AUTHOR
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Labos Elemer, Dec 20 1999
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EXTENSIONS
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More terms from Robert G. Wilson v, Sep 21 2000
Further terms from Naohiro Nomoto, Aug 03 2001
a(26)-a(30) from Donovan Johnson, Dec 21 2008
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STATUS
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approved
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