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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. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 26 07:32 EST 2022. Contains 350577 sequences. (Running on oeis4.)