OFFSET
1,1
COMMENTS
All integers of the form 2^p where 2^p-1 is prime are terms (see A000668). The terms that are not of this form are 320, 11243520. Are there any other? [Edited by Michel Marcus, Nov 22 2022]
a(10) > 10^9. - Michel Marcus, Jan 06 2015
a(11) > 10^10. - Michel Marcus, Nov 22 2022
All terms are even, because odd numbers will fail with A146076(odd) = 0. - Michel Marcus, Nov 22 2022
Numbers k such that A193337(k/2) = k. - Michel Marcus, Nov 23 2022
EXAMPLE
MATHEMATICA
f[n_]:= Plus @@ Select[ Divisors@ n, OddQ]; g[n_]:= Plus @@ Select[ Divisors@ n, EvenQ]; Do[If[f[g[n]]==n, Print[n]], {n, 1, 10^8}]
PROG
(PARI) sod(n) = if (n, sigma(n>>valuation(n, 2)), 0); \\ A000593
sed(n) = if (n%2, 0, 2*sigma(n/2)); \\ A146076
isok(n) = sod(sed(n)) == n;
lista(nn) = forstep(n=2, nn, 2, if(isok(n), print1(n, ", "))); \\ Michel Marcus, Nov 22 2022
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Michel Lagneau, Dec 18 2014
EXTENSIONS
a(10) from Michel Marcus, Nov 22 2022
STATUS
approved