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 A236765 Number of ways to write n = k^2 + m with k > 1 and m > 1 such that sigma(k^2) + prime(m) - 1 is prime, where sigma(j) denotes the sum of all positive divisors of j. 1
 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 0, 2, 3, 1, 3, 2, 1, 2, 2, 3, 2, 4, 3, 2, 3, 2, 2, 3, 3, 2, 2, 2, 3, 4, 4, 3, 4, 4, 1, 3, 4, 2, 2, 5, 3, 3, 4, 4, 3, 1, 5, 3, 4, 3, 4, 5, 4, 3, 1, 5, 2, 6, 4, 3, 4, 2, 1, 5, 4, 7, 4, 4, 3, 1, 3, 1, 4, 4, 4, 2, 5, 6, 3, 6, 5, 5, 1, 4, 5, 5, 4, 3, 6 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,13 COMMENTS Conjecture: (i) If n > 6 is not equal to 18, then a(n) > 0. (ii) Any integer n > 14 can be written as p + q with q > 0 such that p, p + 6 and prime(p) + sigma(q) are all prime. LINKS Zhi-Wei Sun, Table of n, a(n) for n = 1..10000 MAPLE a(10) = 1 since 10 = 2^2 + 6 with sigma(2^2) + prime(6) - 1 = 7 + 13 - 1 = 19 prime. a(253) = 1 since 253 = 15^2 + 28 with sigma(15^2) + prime(28) - 1 = 403 + 107 - 1 = 509 prime. MATHEMATICA p[n_, k_]:=PrimeQ[DivisorSigma[1, k^2]+Prime[n-k^2]-1] a[n_]:=If[n<6, 0, Sum[If[p[n, k], 1, 0], {k, 2, Sqrt[n-2]}]] Table[a[n], {n, 1, 100}] CROSSREFS Cf. A000040, A000203, A233544, A233654, A233793, A233864, A236548. Sequence in context: A349277 A307014 A240871 * A171531 A171532 A171533 Adjacent sequences: A236762 A236763 A236764 * A236766 A236767 A236768 KEYWORD nonn AUTHOR Zhi-Wei Sun, Jan 30 2014 STATUS approved

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Last modified August 15 11:07 EDT 2024. Contains 375173 sequences. (Running on oeis4.)