

A134187


a(0)=1. a(n) = the number of terms of the sequence (from among terms a(0) through a(n1)) which equal any "nonisolated divisors" of (2n). A divisor, k, of n is nonisolated if (k1) or (k+1) also divides n.


3



1, 1, 2, 3, 3, 3, 6, 3, 3, 8, 3, 3, 10, 3, 3, 13, 3, 3, 14, 3, 3, 17, 3, 3, 18, 3, 3, 20, 4, 3, 23, 3, 3, 23, 3, 3, 27, 3, 3, 27, 4, 3, 31, 3, 3, 32, 3, 3, 34, 3, 5, 33, 3, 3, 37, 4, 4, 35, 3, 3, 43, 3, 3, 40, 3, 3, 45, 3, 3, 43, 8, 3, 50, 3, 3, 48, 3, 3, 53, 3, 8, 49, 3, 3, 59, 3, 3, 53, 3, 3, 62, 5
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OFFSET

0,3


LINKS

Antti Karttunen, Table of n, a(n) for n = 0..16384


EXAMPLE

The positive divisors of 2*12=24 are 1,2,3,4,6,8,12,24. Of these, 1,2,3,4 are the nonisolated divisors of 24. There are 2 terms among the earlier terms of the sequence that equal 1, 1 term that equals 2, 7 terms which equal 3 and 0 terms which equal 4. So a(12) = 2+1+7+0 = 10.


PROG

(PARI)
up_to = 91;
A134187list(up_to) = { my(v=vector(1+up_to)); v[1] = 1; for(n=1, up_to, v[1+n] = sum(k=0, n1, my(u=v[1+k]); !((2*n)%u) && ((!((2*n)%(1+u)))  ((u>1)&&(!((2*n)%(u1))))))); (v); };
v134187 = A134187list(up_to);
A134187(n) = v134187[1+n]; \\ Antti Karttunen, Apr 06 2021


CROSSREFS

Cf. A132747, A132881, A134188.
Sequence in context: A131048 A119688 A126868 * A078644 A133700 A087688
Adjacent sequences: A134184 A134185 A134186 * A134188 A134189 A134190


KEYWORD

nonn


AUTHOR

Leroy Quet, Oct 12 2007


EXTENSIONS

Extended by Ray Chandler, Jun 25 2008


STATUS

approved



