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A234399 a(n) = |{0 < k < n:  2^k*(2^{phi(n-k)} - 1) + 1 is prime}|, where phi(.) is Euler's totient function. 3
0, 1, 2, 2, 3, 3, 2, 3, 5, 4, 4, 5, 3, 6, 5, 3, 6, 8, 4, 5, 5, 6, 4, 6, 7, 4, 5, 6, 4, 3, 4, 9, 5, 3, 8, 5, 4, 3, 8, 8, 3, 8, 6, 7, 7, 8, 8, 9, 4, 5, 8, 9, 7, 6, 10, 11, 4, 6, 6, 8, 8, 10, 4, 4, 7, 4, 12, 8, 6, 4, 9, 7, 4, 6, 10, 9, 8, 7, 7, 7, 5, 4, 10, 5, 6, 7, 9, 15, 7, 8, 10, 7, 4, 8, 6, 10, 3, 3, 10, 11 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Conjecture: a(n) > 0 for all n > 1.

See also the conjecture in A234388.

LINKS

Zhi-Wei Sun, Table of n, a(n) for n = 1..4000

EXAMPLE

a(7) = 2 since 2^1*(2^{phi(6)-1) + 1 = 2*3 + 1 = 7 and 2^2*(2^{phi(5)}-1) + 1 = 4*15 + 1 = 61 are both prime.

MATHEMATICA

f[n_, k_]:=f[n, k]=2^k*(2^(EulerPhi[n-k])-1)+1

a[n_]:=Sum[If[PrimeQ[f[n, k]], 1, 0], {k, 1, n-1}]

Table[a[n], {n, 1, 100}]

CROSSREFS

Cf. A000010, A000040, A000079, A234309, A234310, A234337, A234344, A234346, A234347, A234359, A234360, A234361, A234388

Sequence in context: A308621 A308623 A115074 * A214749 A239330 A276273

Adjacent sequences:  A234396 A234397 A234398 * A234400 A234401 A234402

KEYWORD

nonn

AUTHOR

Zhi-Wei Sun, Dec 25 2013

STATUS

approved

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Last modified August 20 02:10 EDT 2019. Contains 326136 sequences. (Running on oeis4.)