

A328238


Quotient A003415(n*m)/A003415(n) for the least m > 1 for which such a quotient is an integer. Here A003415(x) is the arithmetic derivative of x.


2



4, 5, 3, 7, 12, 9, 16, 10, 20, 13, 7, 15, 28, 42, 6, 19, 16, 21, 18, 42, 44, 25, 48, 14, 52, 3, 26, 31, 60, 33, 8, 66, 68, 43, 9, 39, 56, 51, 80, 43, 84, 45, 19, 37, 92, 49, 13, 18, 24, 236, 46, 55, 16, 67, 112, 138, 88, 61, 116, 63, 124, 124, 12, 130, 132, 69, 82, 138, 140, 73, 28, 75, 119, 84, 108, 142, 156, 81, 44, 7, 164
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OFFSET

2,1


LINKS

Antti Karttunen, Table of n, a(n) for n = 2..16385
Antti Karttunen, Data supplement: n, a(n) computed for n = 2..65537


FORMULA

a(n) = A003415(n*A328236(n)) / A003415(n).


EXAMPLE

Arithmetic derivative of 6 is 6' = A003415(6) = 5. Taking arithmetic derivatives of its successive multiples, we obtain 12' = 16, 18' = 21, 24' = 44, 30' = 31, and not until with A003415(6*6) = 36' = 60 we obtain a multiple of 5. Thus a(6) = 60/5 = 12.


PROG

(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A328238(n) = { my(d=A003415(n), t); for(m=2, oo, if(!((t=A003415(n*m))%d), return(t/d))); };


CROSSREFS

Cf. A003415, A328237.
Cf. A328236 (gives the corresponding m).
Sequence in context: A268741 A263031 A004493 * A170929 A245085 A299420
Adjacent sequences: A328235 A328236 A328237 * A328239 A328240 A328241


KEYWORD

nonn


AUTHOR

Antti Karttunen, Oct 08 2019


STATUS

approved



