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A353188
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Number of partitions of n that contain at least one composite part.
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3
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0, 0, 0, 0, 1, 1, 3, 4, 8, 12, 19, 27, 41, 56, 80, 109, 150, 199, 268, 350, 461, 596, 771, 984, 1258, 1589, 2007, 2514, 3145, 3905, 4846, 5973, 7356, 9010, 11020, 13418, 16315, 19756, 23890, 28788, 34639, 41548, 49767, 59441, 70899, 84354, 100221, 118803, 140645, 166153, 196035, 230853, 271512
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OFFSET
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0,7
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LINKS
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FORMULA
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EXAMPLE
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For n = 6 the partitions of 6 that contain at least one composite parts are [6], [4, 2] and [4, 1, 1]. There are three of these partitions so a(6) = 3.
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PROG
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(PARI) a(n) = my(nb=0); forpart(p=n, if (#select(x->((x>1) && !isprime(x)), Vec(p)) >=1, nb++); ); nb; \\ Michel Marcus, Jun 23 2022
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CROSSREFS
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Cf. A000041, A002096, A002808, A023895, A034891, A047967, A085642, A086543, A116449, A144300, A204389.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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