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Search: id:A055773
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| A055773 |
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Product of primes p for which p divides n! but p^2 does not (i.e. ord_p(n!)=1). |
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8
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| 1, 2, 6, 3, 15, 5, 35, 35, 35, 7, 77, 77, 1001, 143, 143, 143, 2431, 2431, 46189, 46189, 46189, 4199, 96577, 96577, 96577, 7429, 7429, 7429, 215441, 215441, 6678671, 6678671, 6678671, 392863, 392863, 392863, 14535931, 765049, 765049, 765049
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Square-free part of n! divided by GCD[Q,F], where Q is the largest square divisor and F is the square-free part of n!. - Labos E. (labos(AT)ana.sote.hu), Jul 12 2000
a(1) = 1, a(n) = n*a(n-1) if n is a prime else a(n) = least integer multiple of a(n-1)/n. - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Apr 29 2004
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LINKS
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F. J. van de Bult, D. C. Gijswijt, J. P. Linderman, N. J. A. Sloane and A. R. Wilks, A Slow-Growing Sequence Defined by an Unusual Recurrence, J. Integer Sequences, Vol. 10 (2007), #07.1.2.
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FORMULA
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a(n) = product of primes p such that n/2 < p <= n. - Klaus Brockhaus, May 02 2004
a(n)=A055204(n)/A055230(n)=A055231(n!)=n!/([A007913(n!)*A055229[n])
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EXAMPLE
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n=13, 13!=6227020800, A007913(13!)=4608*4608, A008833(13!)=3003, g(13!)=GCD(4608,3003)=3, so a(13)=13!/(4608*4608*3)=1001.
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PROGRAM
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(PARI) q=1; for(n=2, 41, print1(q, ", "); q=if(isprime(n), q*n, q/gcd(q, n))) - Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), May 02 2004
(PARI) a(n) = k=1; forprime(p=nextprime(n\2+1), precprime(n), k=k*p); k - Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), May 02 2004
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CROSSREFS
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Cf. A000188, A008833, A007913, A055229, A055231 (for n), A055071, A055204, A055230, A055773 (for n!).
Cf. A094299, A094302.
Adjacent sequences: A055770 A055771 A055772 this_sequence A055774 A055775 A055776
Sequence in context: A094426 A094302 A094300 this_sequence A111866 A072155 A094299
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Jul 12 2000
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EXTENSIONS
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Simpler definition from Dion Gijswijt (gijswijt(AT)science.uva.nl), Jan 07 2007
Entry revised by njas, Jan 07 2007
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