A133565 a(1)=1. a(n+1) = sum{k=non-isolated divisors of n} a(k). A non-isolated divisor, k, of n is a positive divisor of n where (k-1) or (k+1) divides n.

1, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 2, 0, 2, 0, 1, 0, 2, 0, 1, 0, 1, 0, 3, 0, 1, 0, 1, 0, 2, 0, 1, 0, 2, 0, 4, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 2, 0, 3, 0, 1, 0, 3, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 3, 0, 1, 0, 1, 0, 2, 0, 2, 0, 1, 0, 4, 0, 1, 0, 1, 0, 4, 0, 1, 0, 1, 0, 2, 0, 1, 0, 2, 0, 2, 0, 1

Offset

1,7

Comments

a(2n) = 0 since 2n-1 has no non-isolated divisors. - Ray Chandler

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Antti Karttunen, Data supplement: n, a(n) computed for n = 1..100000

Example

The positive divisors of 20 are 1,2,4,5,10,20. Of these, 1 and 2 are adjacent and 4 and 5 are adjacent. So the non-isolated divisors of 20 are 1,2, 4,5. Therefore a(21) = a(1) + a(2) + a(4) + a(5) = 1 + 0 + 0 + 1 = 2.

Prog

(PARI) A133565(n) = if(1==n, n, sumdiv(n-1, d, if((!((n-1)%(1+d))) || ((d>1)&&(!((n-1)%(d-1)))), A133565(d), 0))); \\ Antti Karttunen, Dec 19 2018

Crossrefs

Cf. A132748, A133564.

Sequence in context: A230403 A349907 A248908 * A239704 A168570 A340928

Adjacent sequences: A133562 A133563 A133564 * A133566 A133567 A133568

Keyword

nonn

Author

Leroy Quet, Sep 16 2007

Extensions

Extended by Ray Chandler, Jun 25 2008

Status

approved