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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
OFFSET
1,1
COMMENTS
The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
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.
Sequence in context: A153644 A172437 A160283 * A352481 A019283 A331365
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 02 2019
STATUS
approved