

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, 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
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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}] (* JeanFrançois 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



