A252541 Numbers k such that A146076(A000593(k)) = k.

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

Links

Table of n, a(n) for n=1..10.

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), A146076 (sum of even divisors), A252540.

Sequence in context: A118432 A032404 A059954 * A333103 A139257 A056842

Adjacent sequences: A252538 A252539 A252540 * A252542 A252543 A252544

Keyword

nonn,more

Author

Michel Lagneau, Dec 18 2014

Extensions

a(10) from Michel Marcus, Nov 22 2022

Status

approved