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A086787 a(n) = Sum_{i=1..n} ( Sum_{j=1..n} i^j ). 16
1, 8, 56, 494, 5699, 82200, 1419760, 28501116, 651233661, 16676686696, 472883843992, 14705395791306, 497538872883727, 18193397941038736, 714950006521386976, 30046260016074301944, 1344648068888240941017 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

p divides a(p+1) for all prime p except 3. p^2 divides a(p+1) for prime p in A123374.

2 divides a(n) for n = {2, 3, 4, 6, 7, 8, 10, 11, 12, 14, 15, 16, 18, 19, 20, 22, 23, 24, 26, 27, 28, 30, 31, 32, 34, 35, 36, 38, 39, 40, 42, 43, 44, 46, 47, 48, 50, ...}.

2^2 divides a(n) for n = {2, 3, 6, 7, 8, 10, 11, 14, 15, 16, 18, 19, 22, 23, 24, 26, 27, 30, 31, 32, 34, 35, 38, 39, 40, 42, 43, 46, 47, 48, 50, ...}.

2^3 divides a(n) for n = {2, 3, 6, 7, 10, 11, 14, 15, 16, 18, 19, 22, 23, 26, 27, 30, 31, 32, 34, 35, 38, 39, 42, 43, 46, 47, 48, 50, ...}.

2^4 divides a(n) for n = {7, 14, 15, 18, 23, 30, 31, 32, 34, 39, 46, 47, 50, ...}.

2^5 divides a(n) for n = {15, 30, 31, 34, 47, 62, 63, 64, 66, 79, 94, 95, 98, ...}.

2^6 divides a(n) for n = {31, 62, 63, 66, 95, ...}.

2^7 divides a(n) for n = {63, 126, 127, 130, ...}.

It appears that for k > 2 the least few n such that a(n) is divisible by 2^(k+1) are n = {(2^k-1), 2*(2^k-1), 2*(2^k-1)+1, 2*(2^k-1)+3, 3*(2^k-1)+2, 4*(2^k-1)+2, 4*(2^k-1)+3, 4*(2^k-1)+4, 4*(2^k-1)+6, 5*(2^k-1)+4, 6*(2^k-1)+4, 6*(2^k-1)+5, 6*(2^k-1)+8, ...}. - Alexander Adamchuk, Oct 08 2006

Numbers n that divide a(n) are listed in A014741. - Alexander Adamchuk, Nov 03 2006

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..385

FORMULA

1 - Psi(n) - gamma + Sum_{i=2..n} (i^(n+1)/(i-1)), where Psi(n) is the digamma function and gamma is Euler's constant.

a(n) = Sum[ i^j, {i,1,n}, {j,1,n} ] = n + Sum[ i*(i^n - 1)/(i - 1), {i,2,n} ]. - Alexander Adamchuk, Nov 03 2006

a(n) = Sum_{k=1..n} (B(k+1, n+1) - B(k+1, 1))/(k+1), where B(n, x) are the Bernoulli polynomials. - Daniel Suteu, Jun 25 2018

EXAMPLE

a(2) = 8 = 1 + 1 + 2 + 4 = 1^1 + 1^2 + 2^1 + 2^2.

MAPLE

seq(1-Psi(n)-gamma+sum(i^(n+1)/(i-1), i = 2 .. n), n=1..20);

MATHEMATICA

Table[Sum[i^j, {i, 1, n}, {j, 1, n}], {n, 1, 24}] (* Alexander Adamchuk, Oct 08 2006 *)

Table[ n + Sum[ i*(i^n-1)/(i-1), {i, 2, n} ], {n, 1, 17} ] (* Alexander Adamchuk, Nov 03 2006 *)

PROG

(PARI) a(n)=sum(i=1, n, sum(j=1, n, i^j)) \\ Charles R Greathouse IV, Jul 19 2013

(PARI) a(n)=round(1-psi(n)-Euler+sum(i=2, n, i^(n+1)/(i-1))) \\ Charles R Greathouse IV, Jul 19 2013

CROSSREFS

Cf. A000295, A014741.

Sequence in context: A001398 A251250 A087290 * A218125 A098914 A009107

Adjacent sequences:  A086784 A086785 A086786 * A086788 A086789 A086790

KEYWORD

nonn

AUTHOR

Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Aug 04 2003

EXTENSIONS

Edited by Max Alekseyev, Jan 29 2012

STATUS

approved

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Last modified November 21 01:33 EST 2019. Contains 329349 sequences. (Running on oeis4.)