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

1,1

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

Links

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

Example

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.

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

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

Sequence in context: A254878 A247473 A113479 * A327493 A103970 A227295

Adjacent sequences: A252537 A252538 A252539 * A252541 A252542 A252543

Keyword

nonn,more

Author

Michel Lagneau, Dec 18 2014

Extensions

a(10) from Michel Marcus, Nov 22 2022

Status

approved