A247788 -id:A247788 - cp's OEIS frontend

A247782 Numbers k for which A247781(k+1) = A247781(k).

1, 3, 4, 5, 6, 7, 9, 10, 11, 12, 14, 15, 16, 17, 18, 20, 21, 22, 23, 25, 26, 27, 28, 29, 31, 32, 33, 34, 36, 37, 38, 39, 40, 42, 43, 44, 45, 47, 48, 49, 50, 51, 53, 54, 55, 56, 58, 59, 60, 61, 63, 64, 65, 66, 67, 69, 70, 71, 72, 74, 75, 76, 77, 78, 80, 81

Offset: 1

Clark Kimberling, Sep 24 2014

Every positive integer is in exactly one of the sequences A247782 and A247783.

			The values of 1/e - (1 - 1/k)^k for n = 1..9 are approximately
0.367879, 0.117879, 0.0715831, 0.0514732, 0.0401994, 0.0329815, 0.0279628, 0.0242705, 0.02144, from which we see that the first 9 terms of A247781 are 1,1,2,2,2,2,2,2,3, so that the first six terms of A247782 are 1,3,4,5,6,7.

Clark Kimberling, Table of n, a(n) for n = 1..4000

Cf. A247781, A247783, A247788.

z = 400; f[n_] := f[n] = Select[Range[z], 1/E - (1 - 1/#)^# < 1/n &, 1];
u = Flatten[Table[f[n], {n, 1, z}]] (*A247781*)
d1 = Flatten[Position[Differences[u], 0]] (*A247782*)
d2 = Flatten[Position[Differences[u], 1]] (*A247783*)

A247787 Sum of divisors of 2*prime(n)-1.

Original entry on oeis.org

4, 6, 13, 14, 32, 31, 48, 38, 78, 80, 62, 74, 121, 108, 128, 192, 182, 133, 160, 192, 180, 158, 288, 240, 194, 272, 252, 288, 256, 403, 288, 390, 448, 278, 480, 352, 314, 434, 494, 576, 576, 381, 512, 576, 528, 398, 422, 540, 608, 458, 768, 702, 532, 672

Offset: 1

Jaroslav Krizek, Sep 24 2014

See A005382 (primes p such that sigma(2p-1) = 2p).

			For n = 3; prime(3) = 5, a(3) = sigma(2*5-1) = sigma(9) = 13.

Jens Kruse Andersen, Table of n, a(n) for n = 1..10000

Cf. A000203, A072057, A005382, A247788.

[SumOfDivisors(2*p-1): p in PrimesUpTo(2000)]

vector(100,n,sigma(2*prime(n)-1)) \\ Derek Orr, Sep 25 2014

a(n) = sigma(A076274(n)) = A000203(A076274(n)).

cp's OEIS Frontend

A247782 Numbers k for which A247781(k+1) = A247781(k).

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