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A324521
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Numbers > 1 where the maximum prime index is less than or equal to the number of prime factors counted with multiplicity.
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31
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2, 4, 6, 8, 9, 12, 16, 18, 20, 24, 27, 30, 32, 36, 40, 45, 48, 50, 54, 56, 60, 64, 72, 75, 80, 81, 84, 90, 96, 100, 108, 112, 120, 125, 126, 128, 135, 140, 144, 150, 160, 162, 168, 176, 180, 189, 192, 196, 200, 210, 216, 224, 225, 240, 243, 250, 252, 256
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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 integer partitions with nonnegative rank (A064174). 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}
12: {1,1,2}
16: {1,1,1,1}
18: {1,2,2}
20: {1,1,3}
24: {1,1,1,2}
27: {2,2,2}
30: {1,2,3}
32: {1,1,1,1,1}
36: {1,1,2,2}
40: {1,1,1,3}
45: {2,2,3}
48: {1,1,1,1,2}
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MAPLE
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with(numtheory):
q:= n-> is(pi(max(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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PROG
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(PARI) isok(m) = (m>1) && (primepi(vecmax(factor(m)[, 1])) <= bigomega(m)); \\ Michel Marcus, Nov 14 2022
(Python)
from sympy import factorint, primepi
def ok(n):
f = factorint(n)
return primepi(max(f)) <= sum(f.values())
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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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