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A324560
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Numbers > 1 where the minimum prime index is less than or equal to the number of prime factors counted with multiplicity.
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13
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2, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 26, 27, 28, 30, 32, 33, 34, 36, 38, 39, 40, 42, 44, 45, 46, 48, 50, 51, 52, 54, 56, 57, 58, 60, 62, 63, 64, 66, 68, 69, 70, 72, 74, 75, 76, 78, 80, 81, 82, 84, 86, 87, 88, 90, 92, 93, 94, 96, 98, 99, 100
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OFFSET
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1,1
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COMMENTS
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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.
Also Heinz numbers of a certain type of integer partitions counted by A039900 (but not the type of partitions described in the name). The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
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LINKS
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FORMULA
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EXAMPLE
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The sequence of terms together with their prime indices begins:
2: {1}
4: {1,1}
6: {1,2}
8: {1,1,1}
9: {2,2}
10: {1,3}
12: {1,1,2}
14: {1,4}
15: {2,3}
16: {1,1,1,1}
18: {1,2,2}
20: {1,1,3}
21: {2,4}
22: {1,5}
24: {1,1,1,2}
26: {1,6}
27: {2,2,2}
28: {1,1,4}
30: {1,2,3}
32: {1,1,1,1,1}
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MAPLE
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with(numtheory):
q:= n-> is(pi(min(factorset(n)))<=bigomega(n)):
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MATHEMATICA
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Select[Range[2, 100], PrimePi[FactorInteger[#][[1, 1]]]<=PrimeOmega[#]&]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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