A386248 -id:A386248 - cp's OEIS frontend

A386249 a(n) is the Hamming weight of A161792(n).

1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 6, 1, 1, 2, 1, 1, 2, 1, 1, 2, 6, 1, 1, 2, 1, 1, 2, 1, 1, 2, 6, 1, 14, 1, 2, 15, 1, 1, 2, 1, 1, 2, 6, 1, 1, 2, 1, 1, 2, 1, 1, 2, 6, 1, 1, 2, 1, 14, 1, 2, 1, 15, 1, 2, 6, 1, 1, 2, 1, 1, 2, 1, 19, 1, 2, 6, 1, 1, 2, 1, 1, 2

Offset: 1

Rémy Sigrist, Jul 16 2025

All terms appear infinitely many times: for any n > 0, A161792(n)*2^a(n) also belongs to A161792, say it equals A161792(m) for some m > n, so a(n) = a(m), and we can find as many other occurrences of a(n) as we want.

			a(35) = A000120(2985984) = 6.

Michael S. Branicky, Table of n, a(n) for n = 1..275 (using b-file at A161792)

Cf. A000120, A161792, A325454, A386248.

{ for (n = 1, oo, if (ispower(n, h = hammingweight(n)), print1 (h", "));); }

a(n) = A000120(A161792(n)).

a(65) and beyond from Michael S. Branicky, Jul 21 2025 using A161792

A386290 a(1) = a(2) = 1, and for n > 2, a(n) is the unique k such that A256590(n) = A000120(A256590(n))^k.

Original entry on oeis.org

1, 1, 4, 4, 5, 5, 6, 5, 8, 8, 8, 10, 10, 10, 11, 12, 13, 15, 13, 16, 17, 14, 17, 19, 18, 18, 19, 26, 20, 23, 23, 23, 26, 26, 25, 25, 27, 27, 35, 30, 31, 31, 31, 32, 33, 34, 34, 35, 33, 39, 35, 36, 40, 38, 39, 40, 42, 42, 43, 42, 51, 44, 47, 44, 59, 47, 50, 48

Offset: 1

Rémy Sigrist, Jul 17 2025

			For n = 8: A256590(8) = 59049 = 9^5 = A000120(59049)^5, so a(8) = 5.

Rémy Sigrist, Table of n, a(n) for n = 1..3898
Rémy Sigrist, PARI program

Cf. A000120, A256590, A386248, A386289.

PARI
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A256590(n) = A386289(n)^a(n).

cp's OEIS Frontend

A386249 a(n) is the Hamming weight of A161792(n).

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