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 A112020 Number of partitions of n into distinct semiprimes. 8
 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 2, 0, 0, 1, 2, 2, 1, 0, 1, 3, 2, 2, 1, 2, 3, 5, 2, 2, 3, 5, 4, 5, 3, 4, 6, 9, 6, 5, 6, 10, 10, 9, 7, 9, 12, 14, 12, 11, 14, 18, 17, 16, 16, 19, 21, 24, 21, 23, 26, 29, 30, 32, 31, 33, 39, 40, 39, 41, 45, 49, 54, 53, 54, 59, 68, 66, 68, 70, 78, 82, 88, 86, 93, 101 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,11 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..10000 EXAMPLE For n=4 one partition: {2*2}. For n=6 one partition: {2*3}. For n=10 two partitions: {2*2+2*3,2*5}. MAPLE h:= proc(n) option remember; `if`(n=0, 0, `if`(numtheory[bigomega](n)=2, n, h(n-1))) end: b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0, b(n-i, h(min(n-i, i-1)))+b(n, h(i-1)))) end: a:= n-> b(n, h(n)): seq(a(n), n=0..100); # Alois P. Heinz, Mar 19 2024 MATHEMATICA nmax = 100; CoefficientList[Series[Product[1+x^(Prime[j] Prime[k]), {j, 1, nmax}, {k, j, nmax}], {x, 0, nmax}], x] (* Jean-François Alcover, Nov 10 2021 *) CROSSREFS Cf. A101048, A112022, A001358, A000586. Sequence in context: A205593 A277937 A334913 * A069160 A089616 A089615 Adjacent sequences: A112017 A112018 A112019 * A112021 A112022 A112023 KEYWORD nonn AUTHOR Reinhard Zumkeller, Aug 26 2005 STATUS approved

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Last modified August 14 19:51 EDT 2024. Contains 375167 sequences. (Running on oeis4.)