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 A300580 Number of partitions of n into prime power parts (not including 1) that do not divide n. 3
 1, 0, 0, 0, 0, 1, 0, 3, 1, 3, 2, 11, 1, 18, 6, 9, 5, 43, 5, 65, 7, 31, 30, 137, 5, 115, 59, 84, 26, 379, 19, 519, 42, 213, 197, 323, 23, 1267, 340, 489, 50, 2213, 107, 2897, 221, 375, 938, 4871, 61, 3733, 662, 2193, 553, 10218, 409, 4241, 310, 4341, 3685, 20586, 154, 25792, 5635, 2862, 990, 12806 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 LINKS EXAMPLE a(10) = 2 because we have [7, 3] and [4, 3, 3]. MATHEMATICA Table[SeriesCoefficient[Product[1/(1 - Boole[Mod[n, k] != 0 && PrimePowerQ[k]] x^k), {k, 1, n}], {x, 0, n}], {n, 0, 65}] CROSSREFS Cf. A023894, A098743, A128515, A246655, A284289, A300584. Sequence in context: A133916 A058589 A112164 * A075676 A298262 A124814 Adjacent sequences:  A300577 A300578 A300579 * A300581 A300582 A300583 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Mar 09 2018 STATUS approved

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Last modified May 6 16:17 EDT 2021. Contains 343586 sequences. (Running on oeis4.)