

A124239


a(n) = Sum_{k=1..n} Sum_{m=1..n} (2*k  1)^m.


3



1, 14, 197, 3704, 90309, 2704470, 95856025, 3921108576, 181756280697, 9413656622446, 538727822713277, 33757715581666296, 2298714540642445405, 169016703698449309846, 13345320616706684277361
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OFFSET

1,2


COMMENTS

a(3) = 197 and a(11) = 538727822713277 are primes. p divides a(p+1) for primes p > 3. a(2*k1) is odd. a(2*k) is even. a(2^k) is divisible by 2^(2*k  1) for k > 0.
Numbers n such that a(n) is divisible by n (1, 2, 4, 6, 8, 12, ...) are listed in A124240(n).
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) (136, 408, 620, 680, 820, ...) are listed in A124241(n).


LINKS

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


FORMULA

a(n) = Sum_{k=1..n} Sum_{m=1..n} (2*k  1)^m.
a(n) = n + Sum_{k=2..n} (2*k  1)*((2*k  1)^n  1)/(2*(k  1)).


MATHEMATICA

Table[Sum[(2k1)^m, {k, 1, n}, {m, 1, n}], {n, 1, 20}]


CROSSREFS

Cf. A124240, A124241.
Cf. also A068563, A086787, A123855.
Sequence in context: A067221 A072533 A041085 * A041366 A051817 A199707
Adjacent sequences: A124236 A124237 A124238 * A124240 A124241 A124242


KEYWORD

nonn


AUTHOR

Alexander Adamchuk, Oct 22 2006


STATUS

approved



