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 A325986 Heinz numbers of complete strict integer partitions. 5
 1, 2, 6, 30, 42, 210, 330, 390, 462, 510, 546, 714, 798, 2310, 2730, 3570, 3990, 4290, 4830, 5610, 6006, 6090, 6270, 6510, 6630, 7410, 7590, 7854, 8778, 8970, 9282, 9570, 9690, 10230, 10374, 10626, 11310, 11730, 12090, 12210, 12558, 13398, 13566, 14322, 14430 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Strict partitions are counted by A000009, while complete partitions are counted by A126796. The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k). An integer partition of n is complete (A126796, A325781) if every number from 0 to n is the sum of some submultiset of the parts. The enumeration of these partitions by sum is given by A188431. LINKS FORMULA Intersection of A005117 (strict partitions) and A325781 (complete partitions). EXAMPLE The sequence of terms together with their prime indices begins:       1: {}       2: {1}       6: {1,2}      30: {1,2,3}      42: {1,2,4}     210: {1,2,3,4}     330: {1,2,3,5}     390: {1,2,3,6}     462: {1,2,4,5}     510: {1,2,3,7}     546: {1,2,4,6}     714: {1,2,4,7}     798: {1,2,4,8}    2310: {1,2,3,4,5}    2730: {1,2,3,4,6}    3570: {1,2,3,4,7}    3990: {1,2,3,4,8}    4290: {1,2,3,5,6}    4830: {1,2,3,4,9}    5610: {1,2,3,5,7} MATHEMATICA hwt[n_]:=Total[Cases[FactorInteger[n], {p_, k_}:>PrimePi[p] k]]; Select[Range[1000], SquareFreeQ[#]&&Union[hwt/@Divisors[#]]==Range[0, hwt[#]]&] CROSSREFS Cf. A002033, A056239, A103295, A112798, A126796, A188431, A299702, A304793. Cf. A325780, A325781, A325782, A325788, A325790, A325988. Sequence in context: A166062 A100194 A229882 * A298759 A127517 A137825 Adjacent sequences:  A325983 A325984 A325985 * A325987 A325988 A325989 KEYWORD nonn AUTHOR Gus Wiseman, May 30 2019 STATUS approved

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Last modified June 13 00:57 EDT 2021. Contains 344980 sequences. (Running on oeis4.)