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Search: id:A025528
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| A025528 |
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Number of prime powers <= n with exponents >0. |
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+0
10
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| 0, 1, 2, 3, 4, 4, 5, 6, 7, 7, 8, 8, 9, 9, 9, 10, 11, 11, 12, 12, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 18, 18, 18, 18, 18, 19, 19, 19, 19, 20, 20, 21, 21, 21, 21, 22, 22, 23, 23, 23, 23, 24, 24, 24, 24, 24, 24, 25, 25, 26, 26, 26, 27, 27, 27, 28, 28, 28, 28, 29, 29, 30, 30
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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a(n) = sum of the exponents in the prime factorization of lcm{1,2,...,n}.
Larger than but analogous to Pi(n).
Counts A000961 without 1=prime^0: a(n)=A065515(n)-1. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jul 03 2003
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REFERENCES
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G. Tenenbaum, Introduction a la theorie analytique et probabiliste des nombres, p. 203, Publications de l'Institut Cartan,1990.
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LINKS
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Daniel Forgues, Table of n, a(n) for n=1,...,100000.
Index entries for sequences related to lcm's
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FORMULA
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a(n)=Cardinality[{1, .., n}|A001221(i)=1]
a(n)=sum(p primes <=n, floor(Log(n)/log(p))) - Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 30 2002
a(n) ~ n/log(n) - Benoit Cloitre (benoit7848c(AT)orange.fr), May 30 2003
a(n) = A069637(n) + A000720(n). - Mohammed Bouayoun (bouyao(AT)wanadoo.fr), Feb 24 2004 [Corrected by Franklin T. Adams-Watters, Jun 08 2008]
a(n) = A000720(n) + A000720([n^(1/2)]) + A000720([n^(1/3)]) + ... [From Max Alekseyev (maxale(AT)gmail.com), May 11 2009]
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EXAMPLE
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Below 100 there are 25 primes and 25+10=35 prime powers.
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PROGRAM
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(PARI) for(n=1, 100, print1(sum(k=1, n, floor(log(n)/log(prime(k)))), ", "))
(PARI) a(n)=sum(i=1, n, if(omega(i)-1, 0, 1))
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CROSSREFS
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Cf. A000961, A000040, A000720, A001221, A141228.
Sequence in context: A080820 A116549 A107079 this_sequence A123580 A072894 A037915
Adjacent sequences: A025525 A025526 A025527 this_sequence A025529 A025530 A025531
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KEYWORD
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nonn
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu)
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EXTENSIONS
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New description from Labos E. (labos(AT)ana.sote.hu), Nov 09 2000
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