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A319169 Number of integer partitions of n whose parts all have the same number of prime factors, counted with multiplicity. 13
1, 1, 2, 2, 3, 3, 4, 4, 6, 6, 8, 7, 11, 11, 14, 15, 20, 19, 26, 27, 34, 35, 43, 45, 59, 60, 72, 77, 94, 98, 118, 125, 148, 158, 184, 198, 233, 245, 282, 308, 353, 374, 428, 464, 525, 566, 635, 686, 779, 832, 930, 1005, 1123, 1208, 1345, 1451, 1609, 1732, 1912 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..2500 (first 101 terms from Chai Wah Wu)

EXAMPLE

The a(1) = 1 through a(9) = 6 integer partitions:

  1  2   3    4     5      6       7        8         9

     11  111  22    32     33      52       44        72

              1111  11111  222     322      53        333

                           111111  1111111  332       522

                                            2222      3222

                                            11111111  111111111

MAPLE

b:= proc(n, i, f) option remember; `if`(n=0, 1, `if`(i<1, 0,

      b(n, i-1, f)+(o-> `if`(f in {0, o}, b(n-i, min(i, n-i),

     `if`(f=0, o, f)), 0))(numtheory[bigomega](i))))

    end:

a:= n-> b(n$2, 0):

seq(a(n), n=0..75);  # Alois P. Heinz, Dec 15 2018

MATHEMATICA

Table[Length[Select[IntegerPartitions[n], SameQ@@PrimeOmega/@#&]], {n, 30}]

CROSSREFS

Cf. A000607, A001222, A003963, A064573, A279787, A305551, A319056, A319066, A319071, A320322, A320324.

Sequence in context: A181972 A058747 A034322 * A050365 A029026 A003106

Adjacent sequences:  A319166 A319167 A319168 * A319170 A319171 A319172

KEYWORD

nonn

AUTHOR

Gus Wiseman, Oct 10 2018

EXTENSIONS

a(51)-a(58) from Chai Wah Wu, Nov 12 2018

STATUS

approved

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Last modified February 27 13:18 EST 2020. Contains 332306 sequences. (Running on oeis4.)