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A271319
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Number of distinct prime factors of the n-th n-gonal number (A060354).
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4
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1, 2, 1, 2, 3, 2, 2, 2, 3, 3, 3, 2, 3, 4, 2, 2, 3, 4, 3, 3, 3, 3, 3, 2, 4, 3, 3, 2, 5, 3, 2, 4, 3, 4, 3, 2, 4, 4, 4, 3, 4, 3, 3, 3, 3, 4, 3, 2, 4, 4, 4, 2, 4, 4, 3, 4, 3, 3, 4, 4, 3, 5, 2, 3, 4, 4, 4, 4, 4, 3, 4, 2, 4, 5, 3, 3, 4, 3, 4, 3, 4, 4, 5, 4, 3, 4
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OFFSET
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2,2
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LINKS
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FORMULA
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EXAMPLE
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a(7) = 2 because A060354(7) = 112 = 2^4 * 7^1.
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MATHEMATICA
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Table[PrimeNu[PolygonalNumber[n, n]], {n, 2, 90}] (* Harvey P. Dale, Sep 24 2023 *)
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PROG
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(PARI)
pg(m, n) = (n^2*(m-2)-n*(m-4))/2 \\ n-th m-gonal number
a(n) = omega(pg(n, n))
vector(100, n, n++; a(n))
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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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