1,2

a(3) = 197 and a(11) = 538727822713277 are primes. p divides a(p+1) for prime p>3. a(2k-1) is odd. a(2k) is even. a(2^k) is divisible by 2^(2k-1) for k>0.

Numbers n such that a(n) is divisible by n are listed in A124240[n] = {1, 2, 4, 6, 8, 12, 16, 18, 20, 24, 32, 36, 40, 42, 48, 54, 60, 64, 72, 80, 84, 96, 100, 108, 120, 126, 128, 144, 156, 160, 162, 168, 180, 192, 200, 216, 220, 240, 252, 256, 272, 288, 294, 300, 312, 320, 324, 336, 342, 360, 378, 384, 400, 420, 432, 440, 468, 480, 486, 500, 504, 512, ...}.

It appears that A124240[n] almost coincides with A068563[n] Numbers n such that 2^n (mod n) = 4^n (mod n). The first term that is different is A068563[27] = 136. The terms of A068563[n] that are not the terms of A124240[n] are listed in A124241[n] = {136, 408, 620, 680, 820, ...}.

T. D. Noe, Table of n, a(n) for n=1..100

a(n) = Sum[ Sum[ (2k-1)^m, {m,1,n}], {k,1,n} ]. a(n) = n + Sum[ (2k-1)((2k-1)^n-1) / (2(k-1)), {k,2,n} ].

Table[Sum[(2k-1)^m, {k, 1, n}, {m, 1, n}], {n, 1, 20}]

Cf. A124240, A124241, A068563. Cf. A086787 - Sum(Sum(i^j, j=1..n), i=1..n). Cf. A123855 - Sum[ Sum[ Prime[i]^j, {i, 1, n}], {j, 1, n}].

Sequence in context: A067221 A072533 A041085 this_sequence A041366 A051817 A068769

Adjacent sequences: A124236 A124237 A124238 this_sequence A124240 A124241 A124242

nonn

Alexander Adamchuk (alex(AT)kolmogorov.com), Oct 22 2006