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A061397
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Characteristic function sequence of primes multiplied componentwise by N, the natural numbers.
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12
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0, 2, 3, 0, 5, 0, 7, 0, 0, 0, 11, 0, 13, 0, 0, 0, 17, 0, 19, 0, 0, 0, 23, 0, 0, 0, 0, 0, 29, 0, 31, 0, 0, 0, 0, 0, 37, 0, 0, 0, 41, 0, 43, 0, 0, 0, 47, 0, 0, 0, 0, 0, 53, 0, 0, 0, 0, 0, 59, 0, 61, 0, 0, 0, 0, 0, 67, 0, 0, 0, 71, 0, 73, 0, 0, 0, 0, 0, 79, 0, 0, 0, 83, 0, 0, 0, 0, 0, 89, 0, 0, 0, 0, 0
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Frequently, holes in a sequence are filled with zeros. This is a canonical way to do this and applied here to primes(A000040). A pre-scalar product when summation is omitted.
Equals row sums of triangle A143536 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Aug 23 2008]
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LINKS
| Eric Weisstein's World of Mathematics, Prime zeta function primezeta(s).
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FORMULA
| a(n)=A010051(n)*A000027(n)
Dirichlet generating function: primezeta(s-1). - Franklin T. Adams-Watters, Sep 11 2005.
a(1)=0; for n>=1, a(n)=0, if either p_1|n or p_2|n or...or p_i|n, when n is in [p_i^2,p_(i+1)^2), i=1,2,...,where p_i is the i-th prime; otherwise a(n)=n. [From Vladimir Shevelev (shevelev(AT)bgu.ac.il), Apr 24 2010]
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EXAMPLE
| If 1<n<=8, a(n)=0 iff it is even on interval [4,9); if 9<=n<=25, then a(n)=0 iff n is either even or multiple of 3 on interval [9,25) etc. [From Vladimir Shevelev (shevelev(AT)bgu.ac.il), Apr 24 2010]
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MAPLE
| h:= n->sum(1/k, k=1..n):h2:=n->sum(h(k), k=1..n):seq(((2*n)!* h2(n) mod n^2)/2, n=3..50).[From Gary Detlefs, Oct 29 2011]
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PROG
| (PARI) a(n)=if(isprime(n), n) \\ Charles R Greathouse IV, Oct 29 2011
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CROSSREFS
| Cf. A000040, A010051, A143536.
Sequence in context: A102394 A085563 A071375 * A093438 A047814 A101991
Adjacent sequences: A061394 A061395 A061396 * A061398 A061399 A061400
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KEYWORD
| nonn,easy
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu), Jun 07 2001
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