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 A325708 Numbers n whose prime indices cover an initial interval of positive integers and include all prime exponents of n. 5
 1, 2, 6, 12, 18, 30, 36, 60, 90, 120, 150, 180, 210, 270, 300, 360, 420, 450, 540, 600, 630, 750, 840, 900, 1050, 1080, 1260, 1350, 1470, 1500, 1680, 1800, 1890, 2100, 2250, 2310, 2520, 2700, 2940, 3000, 3150, 3780, 4200, 4410, 4500, 4620, 5040, 5250, 5400 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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 covering an initial interval of positive integers and containing all of their distinct multiplicities. The enumeration of these partitions by sum is given by A325707. LINKS Table of n, a(n) for n=1..49. EXAMPLE The sequence of terms together with their prime indices begins: 1: {} 2: {1} 6: {1,2} 12: {1,1,2} 18: {1,2,2} 30: {1,2,3} 36: {1,1,2,2} 60: {1,1,2,3} 90: {1,2,2,3} 120: {1,1,1,2,3} 150: {1,2,3,3} 180: {1,1,2,2,3} 210: {1,2,3,4} 270: {1,2,2,2,3} 300: {1,1,2,3,3} 360: {1,1,1,2,2,3} 420: {1,1,2,3,4} 450: {1,2,2,3,3} 540: {1,1,2,2,2,3} 600: {1,1,1,2,3,3} MATHEMATICA Select[Range[1000], #==1||Range[PrimeNu[#]]==PrimePi/@First/@FactorInteger[#]&&SubsetQ[PrimePi/@First/@FactorInteger[#], Last/@FactorInteger[#]]&] CROSSREFS Cf. A055932, A109297, A114639, A114640, A181819, A290689, A290822, A325705, A325706, A325707. Sequence in context: A159793 A238739 A006511 * A113274 A181660 A036913 Adjacent sequences: A325705 A325706 A325707 * A325709 A325710 A325711 KEYWORD nonn AUTHOR Gus Wiseman, May 18 2019 STATUS approved

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Last modified February 23 01:47 EST 2024. Contains 370265 sequences. (Running on oeis4.)