A342415 a(n) = phi(n) / gcd(phi(n),A003415(n)), where A003415(n) is the arithmetic derivative of n, and phi is Euler totient function.

1, 1, 2, 1, 4, 2, 6, 1, 1, 4, 10, 1, 12, 2, 1, 1, 16, 2, 18, 1, 6, 10, 22, 2, 2, 4, 2, 3, 28, 8, 30, 1, 10, 16, 2, 1, 36, 6, 3, 4, 40, 12, 42, 5, 8, 22, 46, 1, 3, 4, 8, 3, 52, 2, 5, 6, 18, 28, 58, 4, 60, 10, 12, 1, 8, 20, 66, 4, 22, 24, 70, 2, 72, 12, 8, 9, 10, 24, 78, 2, 1, 40, 82, 6, 32, 14, 7, 2, 88, 8, 18, 11, 30

Offset

1,3

Links

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

Formula

a(n) = A000010(n) / A342413(n) = A000010(n) / gcd(A000010(n),A003415(n)).

a(n) = A173557(n) / A342416(n).

Mathematica

Array[#2/GCD[#1, #2] & @@ {If[# < 2, 0, # Total[#2/#1 & @@@ FactorInteger[#]]] &@ Abs[#], EulerPhi[#]} &, 93] (* 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]));
A342415(n) = { my(u=eulerphi(n)); (u/gcd(u, A003415(n))); };

Crossrefs

Cf. A000010, A003415, A173557, A342009 (positions of ones), A342413, A342414, A342416.

Sequence in context: A217916 A057923 A147763 * A098371 A300234 A070777

Adjacent sequences: A342412 A342413 A342414 * A342416 A342417 A342418

Keyword

nonn

Author

Antti Karttunen, Mar 11 2021

Status

approved