A140608 -id:A140608 - cp's OEIS frontend

A138786 "Left" odd composite numbers n for which n < A140607((n-1)/2).

9, 21, 25, 27, 35, 45, 49, 55, 69, 75, 77, 81, 93, 95, 99, 105, 115, 119, 121, 125, 133, 135, 141, 143, 147, 153, 155, 161, 165, 169, 175, 187, 189, 203, 207, 209, 213, 215, 217, 219, 221, 225, 231, 235, 237, 243, 245, 247, 253, 259, 261, 267, 279, 285, 287

Offset: 1

Vladimir Shevelev, May 18 2008

nonn

There are odd composite numbers which are neither in this sequence nor in A140608. The first such number is 91, see A140667.

Ray Chandler, Table of n, a(n) for n=1..5713

Cf. A140607, A039649, A140140, A138193, A138217, A138227, A138535, A138536, A138537, A138539, A140141, A000010, A000040, A140608, A140667.

Extended by Ray Chandler, May 20 2008

A140607 (A039649(2n+1)+A137576(n))/2.

Original entry on oeis.org

3, 5, 7, 10, 11, 13, 13, 17, 19, 22, 23, 31, 37, 29, 31, 31, 43, 37, 37, 41, 43, 55, 47, 64, 45, 53, 61, 55, 59, 61, 55, 61, 67, 78, 71, 73, 91, 106, 79, 136, 83, 77, 85, 89, 91, 96, 109, 97, 136, 101, 103, 109, 107, 109, 109, 113, 155, 103, 145, 166, 111, 201, 127, 113

Offset: 1

Vladimir Shevelev, May 18 2008

nonn

If 2n+1 is a prime then a(n) = 2n+1.

Ray Chandler, Table of n, a(n) for n=1..10000

Cf. A039649, A137576, A000010, A000040, A140140, A138193, A138217, A138227, A138535, A138536, A138537, A138539, A140141, A140608, A138786, A140667.

Extended by Ray Chandler, May 20 2008, May 24 2008

A140667 Odd composite numbers k for which k = A140607((k-1)/2).

Original entry on oeis.org

91, 1581, 2465, 8481, 25761, 31609, 33355, 34945, 118405, 146611, 319507, 736291, 994507, 3270403, 3375487, 5176153, 6186403, 6228685, 8650951, 10679131, 22028203, 26017291, 31470211, 33796531, 41710411, 42149971, 42474547, 46672291, 48316969, 49019851, 58986091, 68182003, 69885649

Offset: 1

Ray Chandler, May 20 2008

nonn

Cf. A140607, A039649, A140140, A138193, A138217, A138227, A138535, A138536, A138537, A138539, A140141, A000010, A000040, A140608, A138786.

f(n) = (eulerphi(2*n+1) + 1 + g(n))/2; \\ A140607
g(n) = sumdiv(2*n+1, d, eulerphi(d)/(t=znorder(Mod(2, d))))*t-t+1; \\ A137576
isok(c) = if (!isprime(c) && (c%2), f((c-1)/2) == c); \\ Michel Marcus, Jan 31 2023

More terms from Michel Marcus, Jan 31 2023

cp's OEIS Frontend

A138786 "Left" odd composite numbers n for which n < A140607((n-1)/2).

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A140607 (A039649(2n+1)+A137576(n))/2.

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A140667 Odd composite numbers k for which k = A140607((k-1)/2).

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