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 A325131 Heinz numbers of integer partitions where the set of distinct parts is disjoint from the set of distinct multiplicities. 24
 1, 3, 4, 5, 7, 8, 11, 13, 15, 16, 17, 19, 21, 23, 25, 27, 29, 31, 32, 33, 35, 37, 39, 41, 43, 47, 49, 51, 53, 55, 57, 59, 61, 64, 65, 67, 69, 71, 73, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 100, 101, 103, 105, 107, 109, 111, 113, 115, 119, 121, 123, 127 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The enumeration of these partitions by sum is given by A114639. The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k), so these are numbers where the prime indices are disjoint from the prime exponents. LINKS Table of n, a(n) for n=1..63. EXAMPLE The sequence of terms together with their prime indices begins: 1: {} 3: {2} 4: {1,1} 5: {3} 7: {4} 8: {1,1,1} 11: {5} 13: {6} 15: {2,3} 16: {1,1,1,1} 17: {7} 19: {8} 21: {2,4} 23: {9} 25: {3,3} 27: {2,2,2} 29: {10} 31: {11} 32: {1,1,1,1,1} 33: {2,5} MATHEMATICA Select[Range[100], Intersection[PrimePi/@First/@FactorInteger[#], Last/@FactorInteger[#]]=={}&] CROSSREFS Cf. A000720, A001222, A056239, A109298, A112798, A114639, A118914. Cf. A324571, A325127, A325128, A325129, A325130. Sequence in context: A285531 A111801 A108372 * A270342 A066542 A003310 Adjacent sequences: A325128 A325129 A325130 * A325132 A325133 A325134 KEYWORD nonn AUTHOR Gus Wiseman, Apr 01 2019 STATUS approved

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Last modified June 20 03:21 EDT 2024. Contains 373512 sequences. (Running on oeis4.)