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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
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
Sequence in context: A159793 A238739 A006511 * A113274 A181660 A036913
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.)