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 A307373 Heinz numbers of integer partitions with at least three parts, the third of which is 2. 1
 27, 45, 54, 63, 75, 81, 90, 99, 105, 108, 117, 126, 135, 147, 150, 153, 162, 165, 171, 180, 189, 195, 198, 207, 210, 216, 225, 231, 234, 243, 252, 255, 261, 270, 273, 279, 285, 294, 297, 300, 306, 315, 324, 330, 333, 342, 345, 351, 357, 360, 363, 369, 378, 387 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k). The enumeration of these partitions by sum is given by A006918 (see Emeric Deutsch's comment there). LINKS EXAMPLE The sequence of terms together with their prime indices begins: 27: {2,2,2} 45: {2,2,3} 54: {1,2,2,2} 63: {2,2,4} 75: {2,3,3} 81: {2,2,2,2} 90: {1,2,2,3} 99: {2,2,5} 105: {2,3,4} 108: {1,1,2,2,2} 117: {2,2,6} 126: {1,2,2,4} 135: {2,2,2,3} 147: {2,4,4} 150: {1,2,3,3} 153: {2,2,7} 162: {1,2,2,2,2} 165: {2,3,5} 171: {2,2,8} 180: {1,1,2,2,3} MATHEMATICA primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]]; Select[Range[100], PrimeOmega[#]>=3&&Reverse[primeMS[#]][[3]]==2&] CROSSREFS Cf. A000726, A002620, A004250, A006918, A056239, A097701, A112798, A257990, A297113, A325164, A325169, A325170. Sequence in context: A253919 A357077 A259504 * A121614 A046340 A046316 Adjacent sequences: A307370 A307371 A307372 * A307374 A307375 A307376 KEYWORD nonn AUTHOR Gus Wiseman, Apr 05 2019 STATUS approved

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Last modified March 29 20:41 EDT 2023. Contains 361599 sequences. (Running on oeis4.)