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A252541
Numbers k such that A146076(A000593(k)) = k.
1
6, 14, 62, 254, 756, 16382, 262142, 1048574, 39606840, 4294967294
OFFSET
1,1
COMMENTS
All integers of the form 2*(2^p-1) where 2^p-1 is prime are terms (see A139257). The terms that are not of this form are 756, 39606840. Are there any other? [Edited by Michel Marcus, Nov 22 2022]
All terms are even because all terms of A146076 are even. - Michel Marcus, Nov 22 2022
a(11) > 10^10. - Michel Marcus, Nov 22 2022
a(11) > 10^11. - Amiram Eldar, May 19 2024
EXAMPLE
14 is in the sequence because the divisors are {1, 2, 7, 14} => sum of odd divisors 1 + 7 = 8. The divisors of 8 are {1, 2, 4, 8} => sum of even divisors = 2 + 4 + 8 = 14. That is, A146076(A000593(14)) = A146076(8) = 14.
MATHEMATICA
f[n_]:= Plus @@ Select[ Divisors@ n, OddQ]; g[n_]:= Plus @@ Select[ Divisors@ n, EvenQ]; Do[If[g[f[n]]==n, Print[n]], {n, 1, 10^8}]
PROG
(PARI) sod(n) = sigma(n>>valuation(n, 2)); \\ A000593
sed(n) = if (n%2, 0, 2*sigma(n/2)); \\ A146076
isok(n) = sed(sod(n)) == n;
lista(nn) = forstep(n=2, nn, 2, if(isok(n), print1(n, ", "))); \\ Michel Marcus, Nov 22 2022
CROSSREFS
Cf. A000593 (sum of odd divisors), A139257, A146076 (sum of even divisors), A252540.
Sequence in context: A118432 A032404 A059954 * A333103 A139257 A056842
KEYWORD
nonn,more
AUTHOR
Michel Lagneau, Dec 18 2014
EXTENSIONS
a(10) from Michel Marcus, Nov 22 2022
STATUS
approved