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A345744
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Numbers k such that k and k+1 are products of at least 5 primes.
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1
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728, 944, 1215, 1376, 1539, 1700, 2024, 2079, 2295, 2511, 2624, 2672, 3087, 3104, 3159, 3320, 3375, 3807, 3824, 3968, 4095, 4374, 4940, 5103, 5264, 5480, 5535, 5624, 5750, 5775, 5967, 5984, 6075, 6344, 6399, 6560, 6831, 6875, 6975, 6992, 7208, 7424, 7695, 7749, 7856
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OFFSET
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1,1
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COMMENTS
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LINKS
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EXAMPLE
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728 = 2^3*7*13 is a product of 5 primes, while 729 = 3^6 is a product of 6 primes. Thus, 728 is in this sequence.
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MAPLE
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q:= n-> andmap(x-> numtheory[bigomega](x)>4, [n, n+1]):
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MATHEMATICA
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Select[Range[10000], Total[Transpose[FactorInteger[#]][[2]]] > 4 && Total[Transpose[FactorInteger[# + 1]][[2]]] > 4 &]
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PROG
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(Python)
from sympy import factorint
def ok(n): return all(sum(factorint(n+k).values()) > 4 for k in [0, 1])
(PARI) isok(k) = (bigomega(k) >= 5) && (bigomega(k+1) >= 5); \\ Michel Marcus, Jun 26 2021
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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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