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 A061397 Characteristic function sequence of primes multiplied componentwise by N, the natural numbers. 24
 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; text; internal format)
 OFFSET 1,2 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. - Gary W. Adamson, Aug 23 2008 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 Eric Weisstein's World of Mathematics, Prime zeta function primezeta(s). 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. - Vladimir Shevelev, Apr 24 2010 a(n) = n*floor(gcd(((n-1)! + 1)/n,2)). - José de Jesús Camacho Medina, Apr 30 2016 a(n) = n*floor(1/A001065(n)); for n>1. - José de Jesús Camacho Medina, Aug 07 2016 G.f.: x*f'(x), where f(x) = Sum_{k>=1} x^prime(k). - Ilya Gutkovskiy, Apr 10 2017 a(n) = (2n-1)! mod n^2, by Wilson's theorem. - Thomas Ordowski, Dec 27 2017 EXAMPLE If 1 0] & /@ Range@ 94 (* Michael De Vlieger, May 02 2016 *) Table[n*Floor[GCD[((n-1)! + 1)/n, 2]], {n, 2, 100}] (* José de Jesús Camacho Medina, Apr 30 2016 *) PROG (PARI) a(n)=if(isprime(n), n) \\ Charles R Greathouse IV, Oct 29 2011 (Haskell) a061397 n = (fromIntegral \$ a010051 n) * n  -- Reinhard Zumkeller, Mar 21 2014 CROSSREFS Cf. A000040, A010051, A143536. Cf. A034387 (partial sums). Sequence in context: A085563 A071375 A269668 * A093438 A211396 A047814 Adjacent sequences:  A061394 A061395 A061396 * A061398 A061399 A061400 KEYWORD nonn,easy AUTHOR Labos Elemer, Jun 07 2001 STATUS approved

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Last modified April 23 07:51 EDT 2019. Contains 322381 sequences. (Running on oeis4.)