A115964
Denominator of Sum_{i=1..n} 1/prime(i)^3.
Original entry on oeis.org
8, 216, 27000, 9261000, 12326391000, 27081081027000, 133049351085651000, 912585499096480209000, 11103427767506874702903000, 270801499821725167129101267000, 8067447481189014453943055845197000
Offset: 1
1/8, 35/216, 4591/27000, 1601713/9261000, 2141141003/12326391000, 4716413174591/27081081027000.
Cf.
A024451 (numerator of sum_{i=1..n} 1/prime(i)),
A002110 (primorial, also denominator of sum_{i=1..n} 1/prime(i)),
A061015 (numerator of sum_{i=1..n} 1/prime(i)^2).
A061015
Numerator of Sum_{i=1..n} 1/p(i)^2, p(i) = i-th prime.
Original entry on oeis.org
1, 13, 361, 18589, 2293369, 392915461, 114454369129, 41578647715669, 22089188627685001, 18626778064527922741, 17942190650501641587001, 24603083510737933160021269, 41412850736015889039729489289, 76664929233749755566050236079461
Offset: 1
Winston C. Yang (winston(AT)cs.wisc.edu), May 21 2001
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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);
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Numerator[Accumulate[1/Prime[Range[13]]^2]] (* Jayanta Basu, Jul 14 2013 *)
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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
A075986
Numerator of 1+1/prime(1)^2+ ... + 1/prime(n)^2 where prime(k) is the k-th prime.
Original entry on oeis.org
1, 5, 49, 1261, 62689, 7629469, 1294716361, 375074829229, 135662633811769, 71859617272521901, 60483708554835755641, 58166700851687469003901, 79670437976161330893757369, 133981073592392620630139873389
Offset: 0
a(2) = 49 so a(3) = 49*p(3)^2 + (2*3)^2 = 49*25 + 36 = 1261.
- Steven R. Finch, Mathematical Constants, Cambridge, 2003, pp. 94-98.
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Table[Det[DiagonalMatrix[Table[Prime[i]^2,{i,1,n}]]+1],{n,1,15}] (* Alexander Adamchuk, Jul 08 2006 *)
Accumulate[Join[{1},1/Prime[Range[20]]^2]]//Numerator (* Harvey P. Dale, May 08 2023 *)
A115963
Numerator of Sum_{i=1..n} 1/prime(i)^3.
Original entry on oeis.org
1, 35, 4591, 1601713, 2141141003, 4716413174591, 23198819007792583, 159253748925534977797, 1938552948676080555065099, 47290471293028435532185602511, 1409101231790431848106470385672201
Offset: 1
1/8, 35/216, 4591/27000, 1601713/9261000, 2141141003/12326391000, 4716413174591/27081081027000.
Showing 1-4 of 4 results.
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