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 A233566 a(n) = |{0 < p < n: p and p*phi(n-p) - 1 are both prime}|, where phi(.) is Euler's totient function (A000010). 7
 0, 0, 0, 1, 2, 2, 2, 2, 2, 4, 3, 3, 4, 4, 3, 3, 2, 2, 4, 3, 3, 5, 5, 4, 5, 3, 2, 6, 2, 4, 2, 7, 7, 8, 5, 4, 8, 4, 4, 8, 5, 5, 8, 4, 4, 5, 6, 5, 5, 10, 7, 8, 4, 4, 5, 6, 8, 7, 4, 6, 6, 9, 11, 7, 10, 4, 6, 7, 8, 10, 4, 7, 6, 5, 5, 12, 8, 8, 7, 11, 13, 11, 12, 5, 8, 7, 11, 9, 5, 8, 5, 6, 12, 8, 8, 5, 9, 5, 11, 12 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS Conjecture: a(n) > 0 for all n > 3. Also, for any n > 2 there is a prime p < n with p^2*phi(n-p) - 1 prime. LINKS Zhi-Wei Sun, Table of n, a(n) for n = 1..10000 EXAMPLE a(4) = 1 since 3 and 3*phi(4-3) - 1 = 2 are both prime. a(5) = 2 since 2 and 2*phi(5-2) - 1 = 3 are both prime, and also 3 and 3*phi(5-3) - 1 = = 2 are both prime. MATHEMATICA a[n_]:=Sum[If[PrimeQ[Prime[k]*EulerPhi[n-Prime[k]]-1], 1, 0], {k, 1, PrimePi[n-1]}] Table[a[n], {n, 1, 100}] CROSSREFS Cf. A000010, A000040, A233542, A233547, A233549. Sequence in context: A319411 A164296 A319817 * A319818 A319819 A319820 Adjacent sequences: A233563 A233564 A233565 * A233567 A233568 A233569 KEYWORD nonn AUTHOR Zhi-Wei Sun, Dec 13 2013 STATUS approved

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Last modified December 10 17:53 EST 2023. Contains 367713 sequences. (Running on oeis4.)