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.

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

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: A263031 A004493 A348051 * A170929 A245085 A299420

Adjacent sequences: A328235 A328236 A328237 * A328239 A328240 A328241

Keyword

nonn

Author

Antti Karttunen, Oct 08 2019

Status

approved