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A068986
Numbers k such that Sum_{d|k} sigma(d)/d is an integer.
6
1, 21, 105, 1050, 1155, 24921, 26565, 45150, 49842, 59455, 249210, 274131, 548262, 1129645, 1151325, 1248555, 1309350, 2302650, 2741310, 3388935, 4605300, 6305013, 12610026, 13417131, 14685385, 23722545, 25750550, 26834262, 30154410, 33388425, 42997750, 44056155
OFFSET
1,2
COMMENTS
Also numbers k that divide A060640(k). - Seiichi Manyama, May 08 2021
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..100 (terms 1..64 from Michel Marcus)
MATHEMATICA
f[p_, e_] := ((e + 1)*p^(e + 2) - (e + 2)*p^(e + 1) + 1)/(p - 1)^2; q[1] = True; q[n_] := Divisible[Times @@ f @@@ FactorInteger[n], n]; Select[Range[10^6], q] (* Amiram Eldar, Dec 29 2024 *)
PROG
(PARI) for(n=1, 10^7, if(frac(sumdiv(n, d, sigma(d)/d))==0, print1(n, ", ")))
(PARI) is(k) = {my(f = factor(k)); !(prod(i = 1, #f~, p = f[i, 1]; e = f[i, 2]; ((e + 1)*p^(e + 2) - (e + 2)*p^(e + 1) + 1)/(p - 1)^2) % k); } \\ Amiram Eldar, Dec 29 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Benoit Cloitre, Apr 06 2002
EXTENSIONS
More terms from Jason Earls, Apr 09 2002
a(22)-a(25) from Jinyuan Wang, Apr 06 2020
a(26)-a(32) from Michel Marcus, Apr 06 2020
STATUS
approved