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.
A354417
a(n) is the numerator of the sum of the reciprocals of the first n squarefree numbers.
Original entry on oeis.org
1, 3, 11, 61, 11, 82, 171, 1951, 26133, 13424, 41273, 716656, 13871719, 4700888, 9548741, 222854273, 112857219, 3310041496, 20075905417, 628822761157, 19239404599, 9709078632, 1959180271, 73097429088, 147378388979, 445594718515, 18404305970657, 3089336006908, 133763418792581
Offset: 1
1, 3/2, 11/6, 61/30, 11/5, 82/35, 171/70, 1951/770, 26133/10010, 13424/5005, 41273/15015, ...
- Robert Israel, Table of n, a(n) for n = 1..1433
- Sebastian Zuniga Alterman, Explicit averages of square-free supported functions: to the edge of the convolution method, Colloquium Mathematicum, Vol. 168 (2022), pp. 1-23; arXiv preprint, arXiv:2003.05887 [math.NT], 2020.
- Olivier Ramaré, Explicit average orders: news and problems, Banach Center Publications, Vol. 118 (2019), pp. 153-176.
-
s:= 0: R:= NULL: count:= 0:
for x from 1 while count < 40 do
if numtheory:-issqrfree(x) then
s:= s + 1/x;
v:= numer(s);
R:= R, v;
count:= count+1;
fi;
od:
R; # Robert Israel, Mar 05 2023
-
Accumulate[1/Select[Range[43], SquareFreeQ]] // Numerator
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a(n) = my(i=0, s=0); for(x=1, oo, if(core(x)==x, s+=1/x; i++; if(i==n, return(numerator(s))))) \\ Felix Fröhlich, May 26 2022
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