A328236 The least m > 1 such that the arithmetic derivative of m*n is a multiple of the arithmetic derivative of n.

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

Links

Antti Karttunen, Table of n, a(n) for n = 2..16385

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

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

Adjacent sequences: A328233 A328234 A328235 * A328237 A328238 A328239

Keyword

nonn

Author

Antti Karttunen, Oct 08 2019

Status

approved