A252540 Numbers k such that A000593(A146076(k)) = k. (A000593(n) is the sum of the odd divisors of n; A146076(n) is the sum of the even divisors of n.)

4, 8, 32, 128, 320, 8192, 131072, 524288, 11243520, 2147483648

Offset: 1

Author

Michel Lagneau, Dec 18 2014

Keywords

• nonn
• more

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

Examples

			The divisors of 8 are {1, 2, 4, 8}, so the sum of even divisors of 8 is 2 + 4 + 8 = 14, and the divisors of 14 are {1, 2, 7, 14}, so the sum of odd divisors of 14 is 1 + 7 = 8; thus, 8 is in the sequence. That is A000593(A146076(8)) = A000593(14) = 8.
		

Crossrefs

Cf. A000593, A146076, A000668, A193337, A252541.

Programs

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}]

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

Extensions

a(10) from Michel Marcus, Nov 22 2022