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 A325284 Numbers whose prime indices form an initial interval with a single hole: (1, 2, ..., x, x + 2, ..., m - 1, m), where x can be 0 but must be less than m - 1. 4
 3, 9, 10, 15, 20, 27, 40, 42, 45, 50, 70, 75, 80, 81, 84, 100, 105, 126, 135, 140, 160, 168, 200, 225, 243, 250, 252, 280, 294, 315, 320, 330, 336, 350, 375, 378, 400, 405, 462, 490, 500, 504, 525, 560, 588, 640, 660, 672, 675, 700, 729, 735, 756, 770, 800 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798. The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k), so these are Heinz numbers of integer partitions whose distinct parts form an initial interval with a single hole. The enumeration of these partitions by sum is given by A090858. LINKS Table of n, a(n) for n=1..55. EXAMPLE The sequence of terms together with their prime indices begins: 3: {2} 9: {2,2} 10: {1,3} 15: {2,3} 20: {1,1,3} 27: {2,2,2} 40: {1,1,1,3} 42: {1,2,4} 45: {2,2,3} 50: {1,3,3} 70: {1,3,4} 75: {2,3,3} 80: {1,1,1,1,3} 81: {2,2,2,2} 84: {1,1,2,4} 100: {1,1,3,3} 105: {2,3,4} 126: {1,2,2,4} 135: {2,2,2,3} 140: {1,1,3,4} MATHEMATICA Select[Range[100], Length[Complement[Range[PrimePi[FactorInteger[#][[-1, 1]]]], PrimePi/@First/@FactorInteger[#]]]==1&] CROSSREFS Cf. A055932, A056239, A061395, A090858, A112798, A124010, A127002, A130091, A325241, A325251, A325259, A325270. Sequence in context: A191339 A138923 A324584 * A049096 A272653 A030794 Adjacent sequences: A325281 A325282 A325283 * A325285 A325286 A325287 KEYWORD nonn AUTHOR Gus Wiseman, Apr 19 2019 STATUS approved

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Last modified April 20 21:11 EDT 2024. Contains 371845 sequences. (Running on oeis4.)