%I #13 Dec 19 2018 18:51:55

%S 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,

%T 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,

%U 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

%N 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.

%C a(2n) = 0 since 2n-1 has no non-isolated divisors. - _Ray Chandler_

%H Antti Karttunen, <a href="/A133565/b133565.txt">Table of n, a(n) for n = 1..16384</a>

%H Antti Karttunen, <a href="/A133565/a133565.txt">Data supplement: n, a(n) computed for n = 1..100000</a>

%e 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.

%o (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

%Y Cf. A132748, A133564.

%K nonn

%O 1,7

%A _Leroy Quet_, Sep 16 2007

%E Extended by _Ray Chandler_, Jun 25 2008