A152987 Sum of proper divisors minus the number of proper divisors of the number of partitions of n, A000041(n).

0, 0, 0, 0, 0, 0, 6, 11, 35, 47, 57, 16, 0, 98, 187, 146, 176, 184, 525, 326, 1525, 1007, 254, 1632, 1275, 4261, 3311, 2859, 1476, 7489, 4383, 4408, 7624, 9859, 7450, 0, 5428, 9086, 38472, 50191, 29898, 33867, 41264, 22030, 47947, 109323, 107783, 77168

Offset: 1

Author

Omar E. Pol, Dec 21 2008

Keywords

• easy
• nonn

Comments

Note that if a(n) != 0 then the number of partitions of n (A000041(n)) is a composite number (A002808), otherwise A000041(n) is a noncomposite number (A008578). See A152770.

Crossrefs

Cf. A000005, A000041, A000203, A001065, A002808, A008578, A032741, A152770.

Programs

Maple

A000041 := proc(n) combinat[numbpart](n) ; end: A001065 := proc(n) numtheory[sigma](n)-n ; end: A032741 := proc(n) if n = 0 then 0; else numtheory[tau](n)-1 ; fi; end: A152987 := proc(n) local np ; np := A000041(n) ; A001065(np)-A032741(np) ; end: for n from 1 to 80 do printf("%d,",A152987(n)) ; end: # R. J. Mathar, Jan 22 2009

Formula

a(n) = A001065(A000041(n)) - A032741(A000041(n)) = A152770(A000041(n)).

Extensions

More terms from R. J. Mathar, Jan 22 2009