A105732 -id:A105732 - cp's OEIS frontend

A105731 Odd numbers k such that A105658(k) != k.

13, 17, 23, 25, 37, 41, 43, 47, 49, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 75, 77, 81, 83, 85, 97, 99, 103, 107, 111, 117, 121, 123, 125, 127, 129, 131, 137, 139, 143, 145, 149, 151, 153, 157, 159, 161, 163, 169, 173, 177, 179, 181, 183, 189, 191, 193, 195, 197

Offset: 1

Jess E. Boling (tdbpeekitup(AT)yahoo.com) and Robert G. Wilson v, Apr 18 2005

nonn

Cf. A105658, A105732, A105733, A105769.

f[n_] := f[n] = Product[i^i, {i, n}]/Denominator[ Sum[j(j + 1)/2/(Product[j!/k!, {k, 0, j - 1}]), {j, n}]]; Select[ Range[1, 200, 2], f[ # ] != # &]

A105769 a(n) = A105658(n)/k, where k=n if n is odd, else k=n/2.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 1, 1, 13, 55, 1, 1, 1, 1, 1, 175, 325, 13, 253, 1, 1, 1, 1, 1, 23, 1, 1, 1, 1, 5, 1, 1, 19, 11, 19, 5, 35, 1, 1, 629, 1, 253, 29, 1, 1, 29, 31, 43, 37, 5, 13, 43, 1, 1219, 1, 55, 5, 186599, 1, 72283, 1, 29, 1, 47, 1, 1, 1, 1711, 1, 25, 1, 1, 1, 67, 1

Offset: 1

Jess E. Boling (tdbpeekitup(AT)yahoo.com) and Robert G. Wilson v, Apr 18 2005

nonn

Records: 1,11,13,55,175,325,629,1219,186599,6298799,24804047515,..., which occur at: 1,13,16,17,23,24,47,61,65,180,337,...

Cf. A105658, A105731, A105732.

f[n_] := f[n] = Product[i^i, {i, n}]/Denominator[Sum[j(j + 1)/2/(Product[j!/k!, {k, 0, j - 1}]), {j, n}]]; Table[ If[ OddQ[n], f[n]/n, 2f[n]/n], {n, 82}]

A105733 Numbers k such that A105658(2k-1) != 2k-1 and A105658(2k) != k.

Original entry on oeis.org

12, 13, 21, 22, 25, 27, 28, 29, 32, 42, 43, 50, 52, 54, 62, 64, 66, 70, 72, 73, 76, 81, 82, 85, 87, 90, 91, 92, 96, 99, 102, 103, 106, 112, 117, 120, 122, 123, 126, 129, 131, 132, 135, 140, 142, 144, 147, 152, 154, 155, 158, 159, 162, 169

Offset: 1

Jess E. Boling (tdbpeekitup(AT)yahoo.com) and Robert G. Wilson v, Apr 18 2005

nonn

Cf. A105658, A105731, A105732, A105769.

f[n_] := f[n] = Product[i^i, {i, n}]/Denominator[Sum[j(j + 1)/2/(Product[j!/k!, {k, 0, j - 1}]), {j, n}]]; Select[ Range[125], f[2# - 1] != 2# - 1 && f[2# ] != # &]

cp's OEIS Frontend

A105731 Odd numbers k such that A105658(k) != k.

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A105769 a(n) = A105658(n)/k, where k=n if n is odd, else k=n/2.

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A105733 Numbers k such that A105658(2k-1) != 2k-1 and A105658(2k) != k.

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