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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).

%I A060034 #6 Oct 03 2013 11:11:38
%S A060034 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,
%T A060034 170,0,189,43,258,12,372,0,435,82,557,0,808,0,900,162,1150,0,1599,9,
%U A060034 1836,258,2252,0,3111,46,3476,435,4308,0,5827,0,6501,727,7917,85
%N 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).
%F A060034 a(n) = A000041(n) - ( A000837(n) + A024994(n))
%e A060034 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.
%t A060034 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 *)
%Y A060034 A000041, A000837, A024994 and A055892.
%K A060034 easy,nonn
%O A060034 1,10
%A A060034 _Alford Arnold_, Mar 16 2001
%E A060034 More terms from _Naohiro Nomoto_, Mar 01 2002