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

Author

Leroy Quet, Sep 16 2007

Keywords

• nonn

Comments

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

Examples

			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.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..100000

Crossrefs

Cf. A132748, A133564.

Programs

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

Extensions

Extended by Ray Chandler, Jun 25 2008