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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.)