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 A050226 Numbers m such that m divides Sum_{k = 1..m} A000005(k). 28
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 REFERENCES Julian Havil, "Gamma: Exploring Euler's Constant", Princeton University Press, Princeton and Oxford, pp. 112-113, 2003. LINKS Donovan Johnson, Table of n, a(n) for n = 1..39 (quotients <= 40) FORMULA 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. EXAMPLE 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. MATHEMATICA 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 *) PROG (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 CROSSREFS Cf. A000005, A006218, A057494, A085567, A085829. Sequence in context: A304921 A357927 A051721 * A119562 A289021 A323627 Adjacent sequences: A050223 A050224 A050225 * A050227 A050228 A050229 KEYWORD nonn,nice AUTHOR Labos Elemer, Dec 20 1999 EXTENSIONS 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 STATUS approved

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Last modified August 7 08:03 EDT 2024. Contains 375008 sequences. (Running on oeis4.)