A104886 Sequence A048138, the number of times that a positive integer occurs as the sum of proper divisors, if Goldbach partitions (two odd primes, which account for most of the values) are ignored.

0, 1, 1, 0, 2, 1, 2, 0, 1, 0, 1, 1, 2, 1, 2, 0, 1, 0, 2, 1, 2, 0, 1, 0, 1, 0, 1, 0, 1, 2, 2, 1, 1, 0, 1, 0, 1, 0, 3, 1, 2, 1, 2, 0, 2, 0, 1, 1, 2, 0, 0, 0, 2, 1, 1, 2, 1, 0, 1, 0, 2, 1, 3, 1, 1, 0, 1, 0, 1, 0, 1, 2, 3, 0, 3, 0, 1, 0, 1, 2, 1, 0, 1, 0, 1, 1, 0, 1, 2, 0, 2, 0, 1, 0, 0, 2

Offset: 2

Author

Nathan McNew (agreatnate(AT)yahoo.com), Mar 29 2005

Keywords

• nonn

Examples

			a(13)=1 because s(27)=1+3+9 and s(35)=1+5+7=13 however 35's factors 3 and 5 are a Goldbach partition, so 35 is not counted.
		

Crossrefs

Cf. A048138, A001065, A061358.

Formula

a(n) = number of m such that the sum of the proper divisors of m is n, ignoring m if m is the product of two different odd primes.