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A342413 a(n) = gcd(phi(n), A003415(n)), where A003415(n) is the arithmetic derivative of n, and phi is Euler totient function. 7
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 (list; graph; refs; listen; history; text; internal format)
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: A140274 A095231 A303697 * A202019 A295685 A330942

Adjacent sequences:  A342410 A342411 A342412 * A342414 A342415 A342416

KEYWORD

nonn

AUTHOR

Antti Karttunen, Mar 11 2021

STATUS

approved

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Last modified November 28 22:15 EST 2021. Contains 349415 sequences. (Running on oeis4.)