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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(3) = 197 and a(11) = 538727822713277 are primes. p divides a(p+1) for primes p > 3. a(2*k-1) 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[(2k-1)^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

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Last modified August 20 07:48 EDT 2019. Contains 326143 sequences. (Running on oeis4.)