A342458 a(n) = gcd(A001615(n), A003415(n)), where A001615 is Dedekind psi, and A003415 is the arithmetic derivative of n.

1, 1, 1, 2, 1, 1, 1, 12, 6, 1, 1, 8, 1, 3, 8, 8, 1, 3, 1, 12, 2, 1, 1, 4, 10, 3, 9, 16, 1, 1, 1, 16, 2, 1, 12, 12, 1, 3, 8, 4, 1, 1, 1, 24, 3, 1, 1, 16, 14, 45, 4, 28, 1, 27, 8, 4, 2, 1, 1, 4, 1, 3, 3, 96, 6, 1, 1, 36, 2, 1, 1, 12, 1, 3, 5, 40, 6, 1, 1, 16, 108, 1, 1, 4, 2, 3, 8, 4, 1, 3, 4, 48, 2, 1, 24, 16, 1, 7, 3, 20

Offset

1,4

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Formula

a(n) = gcd(A001615(n), A003415(n)).

a(n) = A003557(n) * A342459(n).

a(n) = A003415(n) / A342919(n).

Prog

(PARI)
A001615(n) = if(1==n, n, my(f=factor(n)); prod(i=1, #f~, f[i, 1]^f[i, 2] + f[i, 1]^(f[i, 2]-1))); \\ After code in A001615
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A342458(n) = gcd(A001615(n), A003415(n));

Crossrefs

Cf. A001615, A003415, A003557, A342459, A342919.

Cf. A301939 (gives the positions at which a(n) = A001615(n) = A003415(n)).

Cf. also A175732, A342413, A342915.

Sequence in context: A236938 A079834 A368811 * A358722 A256688 A372326

Adjacent sequences: A342455 A342456 A342457 * A342459 A342460 A342461

Keyword

nonn

Author

Antti Karttunen, Mar 28 2021

Status

approved