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
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