A373364 a(n) = gcd(A001414(n), A003415(n)), where A001414 is the sum of prime factors with repetition, and A003415 is the arithmetic derivative.

0, 1, 1, 4, 1, 5, 1, 6, 6, 7, 1, 1, 1, 9, 8, 8, 1, 1, 1, 3, 10, 13, 1, 1, 10, 15, 9, 1, 1, 1, 1, 10, 14, 19, 12, 10, 1, 21, 16, 1, 1, 1, 1, 3, 1, 25, 1, 1, 14, 3, 20, 1, 1, 1, 16, 1, 22, 31, 1, 4, 1, 33, 1, 12, 18, 1, 1, 3, 26, 1, 1, 12, 1, 39, 1, 1, 18, 1, 1, 1, 12, 43, 1, 2, 22, 45, 32, 1, 1, 1, 20, 3, 34, 49, 24

Offset

1,4

Comments

For n >= 1, a(n) is a multiple of A373363(n).

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Prog

(PARI)
A001414(n) = ((n=factor(n))[, 1]~*n[, 2]); \\ From A001414.
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A373364(n) = gcd(A001414(n), A003415(n));

Crossrefs

Cf. A001414, A003415, A373375 (positions of even terms), A373376 (of odd terms).

Cf. also A082299, A373362, A373363.

Sequence in context: A019303 A339967 A357311 * A107463 A157104 A101322

Adjacent sequences: A373361 A373362 A373363 * A373365 A373366 A373367

Keyword

nonn

Author

Antti Karttunen, Jun 02 2024

Status

approved