

A322986


Number of distinct values obtained when the pibased arithmetic derivative (A258851) is applied to the divisors of n.


1



1, 2, 2, 3, 2, 4, 2, 4, 3, 4, 2, 6, 2, 4, 4, 5, 2, 6, 2, 6, 4, 4, 2, 8, 3, 4, 4, 5, 2, 8, 2, 6, 4, 4, 4, 9, 2, 4, 4, 8, 2, 8, 2, 6, 6, 4, 2, 10, 3, 6, 4, 6, 2, 8, 4, 7, 4, 4, 2, 12, 2, 4, 6, 7, 4, 8, 2, 6, 4, 8, 2, 11, 2, 4, 6, 6, 4, 8, 2, 9, 5, 4, 2, 11, 4, 4, 4, 8, 2, 12, 4, 6, 4, 4, 4, 12, 2, 6, 6, 9, 2, 7, 2, 8, 8
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OFFSET

1,2


LINKS

Antti Karttunen, Table of n, a(n) for n = 1..20160
Antti Karttunen, Data supplement: n, a(n) computed for n = 1..100000
Index entries for sequences computed from indices in prime factorization


FORMULA

a(n) <= A000005(n).


EXAMPLE

Divisors of 28 are [1, 2, 4, 7, 14, 28]. When A258851 is applied to them, we get five distinct values: [0, 1, 4, 4, 15, 44] (because A258851(4) = A258851(7) = 4), thus a(28) = 5, one less than A000005(28)=6.


PROG

(PARI)
A258851(n) = n*sum(i=1, #n=factor(n)~, n[2, i]*primepi(n[1, i])/n[1, i]); \\ From A258851
A322986(n) = { my(m=Map(), s, k=0); fordiv(n, d, if(!mapisdefined(m, s=A258851(d)), mapput(m, s, s); k++)); (k); };
\\ Or maybe more efficiently as, after David A. Corneth's Oct 02 2018 program in A319686:
A322986(n) = { my(d = divisors(n)); for(i=1, #d, d[i] = A258851(d[i])); #Set(d); };


CROSSREFS

Cf. A000005, A258851, A299701, A319686.
Differs from A000005 for the first time at n=28.
Sequence in context: A252505 A325560 A318412 * A167447 A134687 A184395
Adjacent sequences: A322983 A322984 A322985 * A322987 A322988 A322989


KEYWORD

nonn


AUTHOR

Antti Karttunen, Jan 04 2019


STATUS

approved



