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Search: id:A116550
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| A116550 |
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If n = product{p=primes,p|n} p^b(n,p), where each b(n,p) is a positive integer, then a(n) is number of positive integers m, m < n, such that each b(m,p) does not equal b(n,p). |
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+0
1
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| 0, 1, 2, 3, 4, 3, 6, 7, 8, 6, 10, 8, 12, 9, 9, 15, 16, 12, 18, 14, 14, 15, 22, 17, 24, 18, 26, 21, 28, 15, 30, 31, 23, 24, 25, 29, 36, 27, 28, 31, 40, 21, 42, 35, 34, 33, 46, 36, 48, 36, 37, 42, 52, 39, 42, 46, 42, 42, 58, 34, 60, 45, 51, 63, 50, 35, 66, 56, 51, 38, 70, 62, 72, 54
(list; graph; listen)
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OFFSET
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1,3
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EXAMPLE
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12 = 2^2 * 3^1. Of the positive integers < 12, there are 8 integers where no prime divides these integers the same number of times the prime divides 12: 1, 2 = 2^1, 5 = 5^1, 7 = 7^1, 8 = 2^3, 9 = 3^2, 10 = 2^1 *5^1, and 11 = 11^1. So a(12) = 8. The other positive integers < 12 (3 = 3^1, 4 = 2^2, and 6 = 2^1 * 3^1) each are divisible by at least one prime the same number of times this prime divides 12.
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MAPLE
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pAdic := proc(n, p) local f ; for f in ifactors(n)[2] do if op(1, f) = p then RETURN( op(2, f) ) ; fi ; od: RETURN(0) ; end: A027748 := proc(n) [seq(op(1, f), f=ifactors(n)[2])] ; end: A116550 := proc(n) local a, m, nprim, f, p, mgood ; nprim := A027748(n) ; a := 0 ; for m from 1 to n-1 do mgood := true ; for p in nprim do if pAdic(n, p) = pAdic(m, p) then mgood := false ; break ; fi ; od: if mgood then a := a+1 ; fi ; od: RETURN(a) ; end: seq(A116550(n), n=1..90) ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 23 2008
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CROSSREFS
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Sequence in context: A048276 A127463 A076618 this_sequence A116991 A103634 A098596
Adjacent sequences: A116547 A116548 A116549 this_sequence A116551 A116552 A116553
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KEYWORD
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nonn
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AUTHOR
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Leroy Quet (qq-quet(AT)mindspring.com), Mar 16 2006
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 23 2008
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