A305702 a(n) is the denominator of Sum_{primes p < n} 1/(n-p).
1, 1, 1, 2, 6, 12, 20, 10, 84, 840, 72, 630, 1320, 2772, 1560, 90090, 42, 240240, 1904, 46410, 95760, 639540, 5040, 9699690, 637560, 14316120, 92400, 176125950, 308880, 20078358300, 475020, 67690350, 7447440, 116925953760, 110880, 1002802450650, 318240, 122453100, 906665760, 165723680430
Offset: 1
Examples
Sum_{primes p < 6} 1/(6-p) = 1/(6-2) + 1/(6-3) + 1/(6-5) = 19/12 so a(6) = 12.
Links
- Robert Israel, Table of n, a(n) for n = 1..3569
- Math Overflow, Sum of reciprocals of integers minus primes.
Programs
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Maple
N:= 100: # to get a(1)..a(N) P:= select(isprime, [2,seq(i,i=3..N,2)]): seq(denom(add(1/(n-p),p=select(`<`,P,n))), n=1..N);
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PARI
a(n) = my(p=select(x->isprime(x), [1..n-1])); denominator(sum(k=1, #p, 1/(n-p[k]))); \\ Michel Marcus, Jun 09 2018
Comments