A134187 a(0)=1. a(n) = the number of terms of the sequence (from among terms a(0) through a(n-1)) which equal any "non-isolated divisors" of (2n). A divisor, k, of n is non-isolated if (k-1) or (k+1) also divides n.

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

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 non-isolated 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, n-1, my(u=v[1+k]); !((2*n)%u) && ((!((2*n)%(1+u))) || ((u>1)&&(!((2*n)%(u-1))))))); (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