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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.
3
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
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
KEYWORD
nonn
AUTHOR
Antti Karttunen, Oct 08 2019
STATUS
approved