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A090624
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If n=product(pj^ej), i.e. written in its prime factorization, then a(n)=max_j{(pj-1)*ej}.
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3
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1, 2, 2, 4, 2, 6, 3, 4, 4, 10, 2, 12, 6, 4, 4, 16, 4, 18, 4, 6, 10, 22, 3, 8, 12, 6, 6, 28, 4, 30, 5, 10, 16, 6, 4, 36, 18, 12, 4, 40, 6, 42, 10, 4, 22, 46, 4, 12, 8, 16, 12, 52, 6, 10, 6, 18, 28, 58, 4, 60, 30, 6, 6, 12, 10, 66, 16, 22, 6, 70, 4, 72, 36, 8, 18, 10, 12, 78, 4, 8, 40, 82, 6
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,2
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COMMENTS
| The highest power of k dividing n! (A090622) is close to, but below, n/a(k).
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FORMULA
| a(p)=p-1. a(p^m)=(p-1)*m. a(b*c)=max(a(b), a(c)) for b and c coprime.
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EXAMPLE
| 72=2^3*3^2 so a(72)=max((2-1)*3,(3-1)*2)=max(3,4)=4.
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MATHEMATICA
| a[n_] := Module[{aux = FactorInteger[n]}, Max[Table[aux[[i, 2]]*(aux[[i, 1]] - 1), {i, 1, Length[aux]}]]] (* by J.M. Grau Ribas *) [From J.M. Grau Ribas (grau.ribas(AT)uniovi.es), Feb 15 2010]
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CROSSREFS
| Sequence in context: A137502 A143112 A167272 * A099735 A091279 A096002
Adjacent sequences: A090621 A090622 A090623 * A090625 A090626 A090627
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KEYWORD
| nonn
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AUTHOR
| Henry Bottomley (se16(AT)btinternet.com), Dec 06 2003
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