|
|
A245642
|
|
Sum of "number of decompositions of d into ordered sums of two odd primes" over all divisors d of 2*n.
|
|
2
|
|
|
0, 0, 1, 2, 3, 3, 3, 6, 5, 7, 5, 11, 5, 7, 10, 10, 7, 15, 3, 15, 12, 11, 7, 25, 11, 11, 15, 15, 7, 28, 5, 20, 18, 11, 16, 35, 9, 13, 20, 27, 9, 34, 9, 21, 32, 15, 9, 43, 9, 27, 24, 23, 11, 41, 20, 33, 24, 19, 11, 66, 7, 15, 36, 26, 22, 44, 11, 23, 24, 38, 15
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,4
|
|
COMMENTS
|
a(n) is the maximum of the coefficients of polynomial Fn(z) defined in Borwein link as Fn(z) = Sum_{k=0..n-1} (Sum_{j=1..n-1} (isop(j)*z^(k*j))^2), where isop(n) is 1 when n is an odd prime, else 0.
|
|
LINKS
|
|
|
FORMULA
|
a(n) = Sum_{d|2n} A002372(d/2) if d is even.
|
|
MATHEMATICA
|
isop[n_] := Boole[OddQ[n] && PrimeQ[n]];
nbd[n_] := Sum[isop[i]*isop[n-i], {i, 1, n-1}];
a[n_] := Sum[nbd[d], {d, Divisors[2n]}];
|
|
PROG
|
(PARI) isop(n) = (n % 2) && isprime(n);
nbd(n) = sum(i=1, n-1, isop(i)*isop(n-i));
a(n) = sumdiv(2*n, d, nbd(d));
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|