A342413 a(n) = gcd(phi(n), A003415(n)), where A003415(n) is the arithmetic derivative of n, and phi is Euler totient function.

1, 1, 1, 2, 1, 1, 1, 4, 6, 1, 1, 4, 1, 3, 8, 8, 1, 3, 1, 8, 2, 1, 1, 4, 10, 3, 9, 4, 1, 1, 1, 16, 2, 1, 12, 12, 1, 3, 8, 4, 1, 1, 1, 4, 3, 1, 1, 16, 14, 5, 4, 8, 1, 9, 8, 4, 2, 1, 1, 4, 1, 3, 3, 32, 6, 1, 1, 8, 2, 1, 1, 12, 1, 3, 5, 4, 6, 1, 1, 16, 54, 1, 1, 4, 2, 3, 8, 20, 1, 3, 4, 4, 2, 1, 24, 16, 1, 7, 15, 20

Offset

1,4

Links

Antti Karttunen, Table of n, a(n) for n = 1..12500

Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Formula

a(n) = gcd(A000010(n), A003415(n)).

a(n) = A003415(n) / A342414(n) = A000010(n) / A342415(n).

a(n) = A003557(n) * A342416(n).

Mathematica

Array[GCD[If[# < 2, 0, # Total[#2/#1 & @@@ FactorInteger[#]]], EulerPhi[#]] &@ Abs[#] &, 100] (* Michael De Vlieger, Mar 11 2021 *)

Prog

(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A342413(n) = gcd(eulerphi(n), A003415(n));

Crossrefs

Cf. A000010, A003415, A003557, A166374, A342009, A342414, A342415, A342416.

Cf. also A009195, A085731.

Sequence in context: A303697 A362827 A380160 * A202019 A295685 A330942

Adjacent sequences: A342410 A342411 A342412 * A342414 A342415 A342416

Keyword

nonn

Author

Antti Karttunen, Mar 11 2021

Status

approved