1,2

p divides a(p+1) for all prime p except 3. p^2 divides a(p+1) for prime p = {2, 5, 17, 151, ...}. 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 (alex(AT)kolmogorov.com), Oct 08 2006

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

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

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

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

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

Table[Sum[i^j, {i, 1, n}, {j, 1, n}], {n, 1, 24}] - Alexander Adamchuk (alex(AT)kolmogorov.com), Oct 08 2006

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

Cf. A000295, A014741.

Sequence in context: A093134 A001398 A087290 this_sequence A098914 A009107 A133671

Adjacent sequences: A086784 A086785 A086786 this_sequence A086788 A086789 A086790

nonn

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