A342919 - OEIS

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A342919

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

0, 1, 1, 2, 1, 5, 1, 1, 1, 7, 1, 2, 1, 3, 1, 4, 1, 7, 1, 2, 5, 13, 1, 11, 1, 5, 3, 2, 1, 31, 1, 5, 7, 19, 1, 5, 1, 7, 2, 17, 1, 41, 1, 2, 13, 25, 1, 7, 1, 1, 5, 2, 1, 3, 2, 23, 11, 31, 1, 23, 1, 11, 17, 2, 3, 61, 1, 2, 13, 59, 1, 13, 1, 13, 11, 2, 3, 71, 1, 11, 1, 43, 1, 31, 11, 15, 4, 35, 1, 41, 5, 2, 17, 49, 1, 17, 1, 11, 25

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

OFFSET

1,4

LINKS

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

FORMULA

a(n) = A003415(n) / A342458(n) = A003415(n) / gcd(A001615(n), A003415(n)).

a(n) = A342001(n) / A342459(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]));