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

1,7

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.

Links

Table of n, a(n) for n=1..48.

Formula

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

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

Crossrefs

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

Sequence in context: A186410 A192916 A193866 * A100093 A219500 A166702

Adjacent sequences: A152984 A152985 A152986 * A152988 A152989 A152990

Keyword

easy,nonn

Author

Omar E. Pol, Dec 21 2008

Extensions

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

Status

approved