A378518 a(n) = n - A019565(A048675(n)), where A019565 and A048675 are base-2 exp and log-functions.

0, 0, 0, 1, 0, 0, 0, 2, 4, 0, 0, 7, 0, 0, 0, 11, 0, 8, 0, 5, 0, 0, 0, 14, 18, 0, 12, 7, 0, 0, 0, 22, 0, 0, 0, 21, 0, 0, 0, 10, 0, 0, 0, 11, 38, 0, 0, 33, 38, 36, 0, 13, 0, 24, 0, 14, 0, 0, 0, 53, 0, 0, 28, 49, 0, 0, 0, 17, 0, 0, 0, 42, 0, 0, 54, 19, 0, 0, 0, 73, 74, 0, 0, 49, 0, 0, 0, 22, 0, 76, 0, 23, 0, 0, 0, 66, 0, 76

Offset

1,8

Comments

No negative terms because A097246(n) <= n for all n.

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Formula

a(n) = n - A097248(n).

Prog

(PARI)
A097246(n) = { my(f=factor(n)); prod(i=1, #f~, (nextprime(f[i, 1]+1)^(f[i, 2]\2))*((f[i, 1])^(f[i, 2]%2))); };
A097248(n) = { my(k=A097246(n)); while(k<>n, n = k; k = A097246(k)); k; };
A378518(n) = (n - A097248(n));

Crossrefs

Cf. A005117 (positions of 0's), A019565, A048675, A097246, A097248, A376406.

Cf. also A376417, A376418 (analogous sequences for other bases than base-2).

Sequence in context: A230423 A213672 A309244 * A004025 A102561 A072068

Adjacent sequences: A378514 A378516 A378517 * A378519 A378520 A378521

Keyword

nonn,new

Author

Antti Karttunen, Nov 29 2024

Status

approved