A060034 Number of partitions of n such that all parts are neither relatively prime (cf. A000837) nor are they periodic with each part occurring the same number of times (cf. A024994).

0, 0, 0, 0, 0, 0, 0, 1, 0, 3, 0, 4, 0, 9, 3, 12, 0, 22, 0, 28, 9, 43, 0, 63, 3, 82, 19, 107, 0, 170, 0, 189, 43, 258, 12, 372, 0, 435, 82, 557, 0, 808, 0, 900, 162, 1150, 0, 1599, 9, 1836, 258, 2252, 0, 3111, 46, 3476, 435, 4308, 0, 5827, 0, 6501, 727, 7917, 85

Offset

1,10

Links

Table of n, a(n) for n=1..65.

Formula

a(n) = A000041(n) - ( A000837(n) + A024994(n))

Example

a(15) = 3 because partitions 6+3+3+3, 6+6+3 and 9+3+3 satisfy the description and A000041(15) - (A000837(15) + A024994(15)) = 176 - (167 + 6) = 3.

Mathematica

A000837[n_] := Sum[ MoebiusMu[n/d]*PartitionsP[d], {d, Divisors[n]}]; A024994[n_] := Sum[ PartitionsQ[k], {k, Divisors[n] // Most}]; a[n_] := PartitionsP[n] - (A000837[n] + A024994[n]); Table[a[n], {n, 1, 65}] (* Jean-François Alcover, Oct 03 2013 *)

Crossrefs

A000041, A000837, A024994 and A055892.

Sequence in context: A173425 A289445 A237558 * A308216 A035544 A129718

Adjacent sequences: A060031 A060032 A060033 * A060035 A060036 A060037

Keyword

easy,nonn

Author

Alford Arnold, Mar 16 2001

Extensions

More terms from Naohiro Nomoto, Mar 01 2002

Status

approved