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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

Altug Alkan, Table of n, a(n) for n = 1..10000

Peter B. Borwein, Stephen K. K. Choi, Greg Martin, Charles L. Samuels, Polynomials whose reducibility is related to the Goldbach conjecture, arXiv:1408.4881 [math.NT], 2014 (see 3.1 page 7).

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]}];

Array[a, 71] (* Jean-Fran├žois Alcover, Sep 23 2018, translated from PARI *)

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

Cf. A002372.

Sequence in context: A093653 A205442 A049982 * A289559 A070167 A168113

Adjacent sequences:  A245639 A245640 A245641 * A245643 A245644 A245645

KEYWORD

nonn

AUTHOR

Michel Marcus, Aug 22 2014

STATUS

approved

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Last modified May 16 08:04 EDT 2021. Contains 343939 sequences. (Running on oeis4.)