A061015 Numerator of Sum_{i=1..n} 1/p(i)^2, p(i) = i-th prime.

1, 13, 361, 18589, 2293369, 392915461, 114454369129, 41578647715669, 22089188627685001, 18626778064527922741, 17942190650501641587001, 24603083510737933160021269, 41412850736015889039729489289, 76664929233749755566050236079461

Offset: 1

Author

Winston C. Yang (winston(AT)cs.wisc.edu), May 21 2001

Keywords

• easy
• nonn
• frac

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..195

Crossrefs

Cf. A000040, A075986, A075987.

Programs

Maple

summ := 0: for n from 1 to 100 do if (isprime(n)) then summ := summ + 1/n^2; printf("%d,", numer(summ)); #printf("%d,", denom(summ)); end if; od; evalf(summ);

Mathematica

Numerator[Accumulate[1/Prime[Range[13]]^2]] (* Jayanta Basu, Jul 14 2013 *)

Python

from sympy import prime
from fractions import Fraction
from itertools import accumulate, count, islice
def A061015gen(): yield from map(lambda x: x.numerator, accumulate(Fraction(1, prime(k)**2) for k in count(1)))
print(list(islice(A061015gen(), 20))) # Michael S. Branicky, Jun 26 2022

Formula

a(1) = 1; a(n) = a(n-1)*p(n)^2+(p(1)*...*p(n-1))^2. - Zak Seidov, Sep 28 2002

Extensions

a(14) and beyond from Michael S. Branicky, Jun 26 2022