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 A300061 Heinz numbers of integer partitions of even numbers. 13
 1, 3, 4, 7, 9, 10, 12, 13, 16, 19, 21, 22, 25, 27, 28, 29, 30, 34, 36, 37, 39, 40, 43, 46, 48, 49, 52, 53, 55, 57, 61, 62, 63, 64, 66, 70, 71, 75, 76, 79, 81, 82, 84, 85, 87, 88, 89, 90, 91, 94, 100, 101, 102, 107, 108, 111, 112, 113, 115, 116, 117, 118, 120 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k). LINKS Alois P. Heinz, Table of n, a(n) for n = 1..10000 EXAMPLE 75 is the Heinz number of (3,3,2), which has even weight, so 75 belongs to the sequence. Sequence of even-weight partitions begins: () (2) (1,1) (4) (2,2) (3,1) (2,1,1) (6) (1,1,1,1) (8) (4,2) (5,1) (3,3) (2,2,2) (4,1,1). MAPLE a:= proc(n) option remember; local k; for k from 1+      `if`(n=1, 0, a(n-1)) while add(numtheory[pi]       (i[1])*i[2], i=ifactors(k)[2])::odd do od; k     end: seq(a(n), n=1..100);  # Alois P. Heinz, May 22 2018 MATHEMATICA Select[Range[200], EvenQ[Total[Cases[FactorInteger[#], {p_, k_}:>k*PrimePi[p]]]]&] CROSSREFS Complement of A300063. Cf. A000041, A000720, A001222, A056239, A063834, A100118, A112798, A122111, A215366, A296150, A299202, A299757, A300056, A300060, A304662. Sequence in context: A037988 A213508 A088958 * A300789 A026225 A026140 Adjacent sequences:  A300058 A300059 A300060 * A300062 A300063 A300064 KEYWORD nonn AUTHOR Gus Wiseman, Feb 23 2018 STATUS approved

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Last modified March 30 12:10 EDT 2020. Contains 333125 sequences. (Running on oeis4.)