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Search: id:A091137
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| A091137 |
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Largest number m such that number of times m divides k! is almost k/n for large k, i.e. largest m with A090624(m)=n. |
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25
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| 1, 2, 12, 24, 720, 1440, 60480, 120960, 3628800, 7257600, 479001600, 958003200, 2615348736000, 5230697472000, 31384184832000, 62768369664000, 32011868528640000, 64023737057280000, 51090942171709440000
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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P. Curtz, Integration numerique ..., Note 12, C.C.S.A., Arcueil, 1969; see pp. 36, 56.
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FORMULA
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a(n) = product_p{p prime} p^floor[n/(p-1)]. a(2n+1) = 2*a(2n).
a(n+1)=A027760(n+1)*a(n). - Paul Curtz (bpcrtz(AT)free.fr), Aug 01 2008
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EXAMPLE
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a(2) = 12 noting that 100! is a multiple of 12^48 and 48 is almost 100/2.
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MAPLE
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A091137 := proc(n) local a, i, p ; a := 1 ; for i from 1 do p := ithprime(i) ; if p > n+1 then break; fi; a := a*p^floor(n/(p-1)) ; od: a ; end: for n from 0 to 20 do printf("%a, ", A091137(n) ) ; od: [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 23 2009]
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CROSSREFS
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Starts similarly to A002207 especially for even n and all values of A002207 seen so far seem to divide a(n). Cf. A090622, A090624, A091136.
Sequence in context: A141900 A126962 A002207 this_sequence A092825 A135396 A031048
Adjacent sequences: A091134 A091135 A091136 this_sequence A091138 A091139 A091140
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KEYWORD
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nonn
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), Dec 19 2003
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