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A161116
a(n) is the number of nontrivial positive divisors of 2n+3.
1
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
0,7
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.
FORMULA
For n>=1, a(n)=A160973(n)+A079978(n). [Vladimir Shevelev, Jun 07 2009]
a(n) = A070824(2n+3).
EXAMPLE
Since for n=3 we have 2n+3=9 and only nontrivial divisor of 9 is 3, then a(3)=1.
PROG
(PARI) a(n) = numdiv(2*n+3) - 2; \\ Michel Marcus, Feb 08 2016
(Magma) [NumberOfDivisors(2*n+3)-2: n in [0..100]]; // Vincenzo Librandi, Feb 08 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vladimir Shevelev, Jun 02 2009
EXTENSIONS
Edited by Charles R Greathouse IV, Oct 12 2009
More terms from Michel Marcus, Feb 08 2016
STATUS
approved