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A328236
The least m > 1 such that the arithmetic derivative of m*n is a multiple of the arithmetic derivative of n.
5
2, 2, 2, 2, 6, 2, 8, 4, 10, 2, 4, 2, 14, 12, 4, 2, 10, 2, 8, 21, 22, 2, 24, 4, 26, 2, 12, 2, 30, 2, 6, 33, 34, 8, 6, 2, 18, 12, 40, 2, 42, 2, 8, 22, 46, 2, 10, 4, 14, 32, 33, 2, 8, 12, 56, 24, 30, 2, 56, 2, 62, 40, 8, 65, 66, 2, 65, 69, 70, 2, 22, 2, 45, 24, 32, 65, 78, 2, 24, 4, 82, 2, 30, 24, 50, 16, 88, 2, 42, 32, 20, 40
OFFSET
2,1
EXAMPLE
Arithmetic derivative of 6 is 6' = A003415(6) = 5. Taking arithmetic derivatives of successive multiples of six 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) = 6.
PROG
(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A328236(n) = { my(d=A003415(n)); for(m=2, oo, if(!(A003415(n*m)%d), return(m))); };
CROSSREFS
Cf. A003415, A328235, A328238 (gives the corresponding quotients).
Sequence in context: A349923 A080400 A351031 * A119462 A293221 A334512
KEYWORD
nonn
AUTHOR
Antti Karttunen, Oct 08 2019
STATUS
approved