A328235 The least k > 0 such that the arithmetic derivative of n+k is a multiple of the arithmetic derivative of n.

1, 1, 4, 1, 15, 1, 12, 11, 8, 1, 4, 1, 13, 1, 12, 1, 20, 1, 24, 4, 23, 1, 56, 7, 10, 27, 36, 1, 28, 1, 44, 15, 114, 1, 76, 1, 84, 5, 56, 1, 48, 1, 20, 27, 53, 1, 80, 3, 36, 25, 76, 1, 81, 9, 4, 23, 26, 1, 116, 1, 64, 207, 80, 3, 52, 1, 40, 3, 82, 1, 232, 1, 205, 31, 36, 4, 27, 1, 92, 27, 88, 1, 160, 36, 130, 5, 12, 1, 81, 9, 52, 3

Offset

2,3

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 A003415(6) = 5. Not until at k=21 we find another number whose arithmetic derivative is a multiple of five (as A003415(21) = 10 = 2*5), thus a(6) = 21-6 = 15.

Prog

(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A328235(n) = { my(d=A003415(n)); for(k=1, oo, if(!(A003415(n+k)%d), return(k))); };

Crossrefs

Cf. A003415, A328236, A328237 (gives the quotient).

Sequence in context: A353763 A226478 A349124 * A293129 A200062 A338832

Adjacent sequences: A328232 A328233 A328234 * A328236 A328237 A328238

Keyword

nonn

Author

Antti Karttunen, Oct 08 2019

Status

approved