A328237 Quotient A003415(n+k)/A003415(n) for the least k > 0 for which such a quotient is an integer. Here A003415(x) is the arithmetic derivative of x.

1, 4, 3, 5, 2, 12, 2, 4, 3, 16, 2, 9, 3, 4, 1, 21, 1, 24, 2, 1, 3, 44, 4, 8, 4, 3, 6, 31, 1, 80, 1, 8, 8, 5, 4, 21, 3, 3, 4, 41, 3, 48, 4, 4, 3, 112, 4, 4, 1, 4, 8, 81, 2, 12, 1, 8, 4, 92, 4, 33, 5, 9, 2, 4, 1, 72, 3, 6, 4, 156, 4, 39, 5, 1, 3, 6, 1, 176, 1, 2, 3, 124, 2, 1, 12, 3, 1, 123, 1, 7, 4, 8, 3, 9, 1, 77, 3, 1, 4

Offset

2,2

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+A328235(n)) / A003415(n).

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) = 10/5 = 2.

Prog

(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A328237(n) = { my(d=A003415(n), t); for(k=1, oo, if(!((t=A003415(n+k))%d), return(t/d))); };

Crossrefs

Cf. A003415, A328235 (gives the corresponding k).

Sequence in context: A321154 A011206 A326768 * A249220 A075128 A074091

Adjacent sequences: A328234 A328235 A328236 * A328238 A328239 A328240

Keyword

nonn

Author

Antti Karttunen, Oct 08 2019

Status

approved