

A319686


Number of distinct values obtained when arithmetic derivative (A003415) is applied to the divisors of n.


5



1, 2, 2, 3, 2, 3, 2, 4, 3, 3, 2, 5, 2, 3, 3, 5, 2, 5, 2, 5, 3, 3, 2, 7, 3, 3, 4, 5, 2, 6, 2, 6, 3, 3, 3, 8, 2, 3, 3, 7, 2, 6, 2, 5, 5, 3, 2, 9, 3, 5, 3, 5, 2, 7, 3, 7, 3, 3, 2, 10, 2, 3, 5, 7, 3, 6, 2, 5, 3, 6, 2, 11, 2, 3, 5, 5, 3, 6, 2, 9, 5, 3, 2, 10, 3, 3, 3, 7, 2, 10, 3, 5, 3, 3, 3, 11, 2, 5, 5, 8, 2, 6, 2, 7, 6, 3, 2, 11, 2, 6, 3, 8, 2, 6, 3, 5, 5, 3, 3, 14
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OFFSET

1,2


LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65537


FORMULA

a(n) = 1+A319685(n).


PROG

(PARI)
A003415(n) = {my(fac); if(n<1, 0, fac=factor(n); sum(i=1, matsize(fac)[1], n*fac[i, 2]/fac[i, 1]))}; \\ From A003415
A319686(n) = { my(m=Map(), s, k=0); fordiv(n, d, if(!mapisdefined(m, s=A003415(d)), mapput(m, s, s); k++)); (k); };
(PARI) a(n) = my(d = divisors(n)); for(i = 1, #d, d[i] = A003415(d[i])); #Set(d) \\ uses A003415 listed at Antti's programs. David A. Corneth, Oct 02 2018


CROSSREFS

One more than A319685.
Cf. A003415.
Cf. also A184395, A319696.
Sequence in context: A088873 A085082 A181796 * A326082 A067554 A135981
Adjacent sequences: A319683 A319684 A319685 * A319687 A319688 A319689


KEYWORD

nonn


AUTHOR

Antti Karttunen, Oct 02 2018


STATUS

approved



