A300253 GCD of arithmetic derivative (A003415) and its Möbius transform (A300251).

0, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 8, 1, 1, 2, 4, 1, 1, 1, 2, 2, 1, 1, 4, 1, 1, 3, 4, 1, 1, 1, 16, 2, 1, 2, 4, 1, 1, 2, 4, 1, 1, 1, 16, 13, 1, 1, 16, 1, 1, 2, 2, 1, 3, 2, 4, 2, 1, 1, 4, 1, 1, 3, 16, 2, 1, 1, 2, 2, 1, 1, 4, 1, 1, 1, 8, 2, 1, 1, 88, 27, 1, 1, 4, 2, 1, 2, 28, 1, 1, 2, 4, 2, 1, 2, 16, 1, 11, 1, 2, 1, 1, 1, 4, 1

Offset

1,8

Links

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

Formula

a(n) = gcd(A003415(n), A300251(n)) = gcd(A003415(n), A300252(n)).

Prog

(PARI)
A003415(n) = {my(fac); if(n<1, 0, fac=factor(n); sum(i=1, matsize(fac)[1], n*fac[i, 2]/fac[i, 1]))}; \\ From A003415
A300251(n) = sumdiv(n, d, moebius(n/d)*A003415(d));
A300253(n) = gcd(A003415(n), A300251(n));

Crossrefs

Cf. A003415, A085731, A300245, A300251, A300252.

Sequence in context: A308552 A368333 A088440 * A212173 A366993 A274006

Adjacent sequences: A300250 A300251 A300252 * A300254 A300255 A300256

Keyword

nonn

Author

Antti Karttunen, Mar 08 2018

Status

approved