

A328235


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


5



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
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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) = 216 = 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: A016115 A164794 A226478 * A293129 A200062 A229468
Adjacent sequences: A328232 A328233 A328234 * A328236 A328237 A328238


KEYWORD

nonn


AUTHOR

Antti Karttunen, Oct 08 2019


STATUS

approved



