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Search: id:A069212
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| A069212 |
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a(n)=sum(k=1,n,3^omega(k)). |
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+0
1
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| 1, 4, 7, 10, 13, 22, 25, 28, 31, 40, 43, 52, 55, 64, 73, 76, 79, 88, 91, 100, 109, 118, 121, 130, 133, 142, 145, 154, 157, 184, 187, 190, 199, 208, 217, 226, 229, 238, 247, 256, 259, 286, 289, 298, 307, 316, 319, 328, 331, 340, 349, 358, 361, 370, 379, 388, 397
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OFFSET
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1,2
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COMMENT
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More generally, if b is an integer =>3, sum(k=1,n,b^omega(k))~C(b)*n*ln(n)^(b-1) where C(b)=1/(b-1)!*prod((1-1/p)^(b-1)*(1+(b-1)/p))
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REFERENCES
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G. Tenenbaum and Jie Wu, Cours Specialises No. 2: "Theorie analytique et probabiliste des nombres", Collection SMF, Ordres moyens, p. 20.
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FORMULA
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Asymptotic formula : a(n)~C*n*ln(n)^2 with C= (1/2) *prod((1-1/p)^2*(1+2/p)) where the product is over all the primes.
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CROSSREFS
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Sequence in context: A008470 A002640 A096675 this_sequence A091290 A119256 A143454
Adjacent sequences: A069209 A069210 A069211 this_sequence A069213 A069214 A069215
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KEYWORD
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easy,nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 14 2002
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