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 A325994 Heinz numbers of integer partitions such that not every ordered pair of distinct parts has a different quotient. 13
 42, 84, 126, 168, 210, 230, 252, 294, 336, 378, 390, 399, 420, 460, 462, 504, 546, 588, 630, 672, 690, 714, 742, 756, 780, 798, 840, 882, 920, 924, 966, 1008, 1050, 1092, 1134, 1150, 1170, 1176, 1197, 1218, 1260, 1302, 1344, 1365, 1380, 1386, 1428, 1470, 1484 (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). LINKS EXAMPLE The sequence of terms together with their prime indices begins:     42: {1,2,4}     84: {1,1,2,4}    126: {1,2,2,4}    168: {1,1,1,2,4}    210: {1,2,3,4}    230: {1,3,9}    252: {1,1,2,2,4}    294: {1,2,4,4}    336: {1,1,1,1,2,4}    378: {1,2,2,2,4}    390: {1,2,3,6}    399: {2,4,8}    420: {1,1,2,3,4}    460: {1,1,3,9}    462: {1,2,4,5}    504: {1,1,1,2,2,4}    546: {1,2,4,6}    588: {1,1,2,4,4}    630: {1,2,2,3,4}    672: {1,1,1,1,1,2,4} MATHEMATICA Select[Range[1000], !UnsameQ@@Divide@@@Subsets[PrimePi/@First/@FactorInteger[#], {2}]&] CROSSREFS The subset case is A325860. The maximal case is A325861. The integer partition case is A325853. The strict integer partition case is A325854. Heinz numbers of the counterexamples are given by A325994. Cf. A002033, A056239, A103300, A108917, A112798, A143823, A196724, A325768, A325856, A325868, A325869, A325876. Sequence in context: A153644 A172437 A160283 * A019283 A331365 A300603 Adjacent sequences:  A325991 A325992 A325993 * A325995 A325996 A325997 KEYWORD nonn AUTHOR Gus Wiseman, Jun 02 2019 STATUS approved

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Last modified January 18 07:55 EST 2022. Contains 350454 sequences. (Running on oeis4.)