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A096624
Numerators of the Riemann prime counting function.
5
0, 1, 2, 5, 7, 7, 9, 29, 16, 16, 19, 19, 22, 22, 22, 91, 103, 103, 115, 115, 115, 115, 127, 127, 133, 133, 137, 137, 149, 149, 161, 817, 817, 817, 817, 817, 877, 877, 877, 877, 937, 937, 997, 997, 997, 997, 1057, 1057, 1087, 1087, 1087, 1087, 1147, 1147, 1147
OFFSET
1,3
LINKS
Eric Weisstein's World of Mathematics, Riemann Prime Counting Function
FORMULA
Let Sk{f(k)}= Sum_{k>=2}f(k), then the g.f. of A096624/A096625 can be written as
(1/1)*Sa{(x^a)/(1-x)} - (1/2)*Sa{ Sb{ (x^(a*b))/(1-x)}} + (1/3)*Sa{ Sb{ Sc{ (x^(a*b*c))/(1-x)}}} - (1/4)*Sa{ Sb{ Sc{ Sd{ (x^(a*b*c*d))/(1-x)}}}} + ... . - Mats Granvik, Apr 06 2011
EXAMPLE
0, 1, 2, 5/2, 7/2, 7/2, 9/2, 29/6, 16/3, 16/3, 19/3, ...
MATHEMATICA
Table[Sum[PrimePi[x^(1/k)]/k, {k, Log2[x]}], {x, 100}] // Numerator (* Eric W. Weisstein, Jan 09 2019 *)
PROG
(PARI) a(n) = numerator(sum(k=1, n, if (p=isprimepower(k), 1/p))); \\ Michel Marcus, Jan 07 2019
(PARI) a(n) = numerator(sum(k=1, logint(n, 2), primepi(sqrtnint(n, k))/k)); \\ Daniel Suteu, Jan 07 2019
CROSSREFS
Cf. A096625.
Sequence in context: A131688 A226213 A199590 * A145378 A069887 A254340
KEYWORD
nonn,frac
AUTHOR
Eric W. Weisstein, Jul 01 2004
STATUS
approved