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A138217
Odd numbers n for which A137576((n-1)/2)-1 is a multiple of A000010(n).
6
1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 23, 25, 27, 29, 31, 33, 37, 39, 41, 43, 47, 49, 53, 55, 57, 59, 61, 63, 67, 71, 73, 79, 81, 83, 87, 89, 95, 97, 101, 103, 107, 109, 111, 113, 119, 121, 125, 127, 131, 135, 137, 139, 143, 149, 151, 153, 157, 159, 161, 163, 167, 169, 173
OFFSET
1,2
COMMENTS
The sequence contains all odd primes. Indeed, if p is a prime then A137576((p-1)/2)-1=p-1=A000010(p).
Conjecture: the sequence contains infinitely many composite numbers.
The conjecture is true because of the sequence contains all powers of odd primes. Indeed, A137576((P^k-1)/2)-1=k*A000010(p^k). - Vladimir Shevelev, May 29 2008
LINKS
MATHEMATICA
A137576[n_] := Module[{t}, (t = MultiplicativeOrder[2, 2 n + 1])* DivisorSum[2 n + 1, EulerPhi[#]/MultiplicativeOrder[2, #] &] - t + 1];
okQ[n_] := OddQ[n] && Divisible[A137576[(n - 1)/2] - 1, EulerPhi[n]];
Reap[For[k = 1, k < 200, k += 2, If[okQ[k], Sow[k]]]][[2, 1]] (* Jean-François Alcover, Jan 11 2019 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Shevelev, May 05 2008
EXTENSIONS
Extended by Ray Chandler, May 08 2008
STATUS
approved