A161116 a(n) is the number of nontrivial positive divisors of 2n+3.

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, 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, 0, 2, 2, 2, 4, 0, 0, 4, 2, 0, 2, 2, 0, 6, 0, 1, 4, 0, 4, 2, 0, 0, 2

Offset: 0

Author

Vladimir Shevelev, Jun 02 2009

Keywords

• nonn
• easy

Comments

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.

Examples

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

Crossrefs

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

Cf. A160973. - Vladimir Shevelev, Jun 07 2009

Programs

Magma

[NumberOfDivisors(2*n+3)-2: n in [0..100]]; // Vincenzo Librandi, Feb 08 2016

PARI

a(n) = numdiv(2*n+3) - 2; \\ Michel Marcus, Feb 08 2016

Formula

For n>=1, a(n)=A160973(n)+A079978(n). [Vladimir Shevelev, Jun 07 2009]

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

Extensions

Edited by Charles R Greathouse IV, Oct 12 2009

More terms from Michel Marcus, Feb 08 2016