A134187 - OEIS

%I #13 Apr 06 2021 15:06:29

%S 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,

%T 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,

%U 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

%N 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.

%H Antti Karttunen, <a href="/A134187/b134187.txt">Table of n, a(n) for n = 0..16384</a>

%e 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.

%o (PARI)

%o up_to = 91;

%o 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); };

%o v134187 = A134187list(up_to);

%o A134187(n) = v134187[1+n]; \\ _Antti Karttunen_, Apr 06 2021

%Y Cf. A132747, A132881, A134188.

%K nonn

%O 0,3

%A _Leroy Quet_, Oct 12 2007

%E Extended by _Ray Chandler_, Jun 25 2008