A161116 - OEIS

%I #13 Sep 08 2022 08:45:45

%S 0,0,0,1,0,0,2,0,0,2,0,1,2,0,0,2,2,0,2,0,0,4,0,1,2,0,2,2,0,0,4,2,0,2,

%T 0,0,4,2,0,3,0,2,2,0,2,2,2,0,4,0,0,6,0,0,2,0,2,4,2,1,2,2,0,2,0,2,6,0,

%U 0,2,2,2,4,0,0,4,2,0,2,2,0,6,0,1,4,0,4,2,0,0,2

%N a(n) is the number of nontrivial positive divisors of 2n+3.

%C a(n)=0 iff n is in A067076, i.e., 2n+3 is prime; a(n) is the number of positive integers of the form (n-3k)/(2k+1), 1<=k<=n/3.

%F For n>=1, a(n)=A160973(n)+A079978(n). [_Vladimir Shevelev_, Jun 07 2009]

%F a(n) = A070824(2n+3).

%e Since for n=3 we have 2n+3=9 and only nontrivial divisor of 9 is 3, then a(3)=1.

%o (PARI) a(n) = numdiv(2*n+3) - 2; \\ _Michel Marcus_, Feb 08 2016

%o (Magma) [NumberOfDivisors(2*n+3)-2: n in [0..100]]; // _Vincenzo Librandi_, Feb 08 2016

%Y Cf. A067076, A034953, A054269, A082749, A006254.

%Y Cf. A160973. - _Vladimir Shevelev_, Jun 07 2009

%K nonn,easy

%O 0,7

%A _Vladimir Shevelev_, Jun 02 2009

%E Edited by _Charles R Greathouse IV_, Oct 12 2009

%E More terms from _Michel Marcus_, Feb 08 2016