A290347 Numerators of the Harary index for the n-halved cube graph.

0, 1, 6, 26, 100, 1096, 3920, 13936, 16544, 296256, 1068672, 11652352, 42658304, 1100471296, 4079876096, 15205967872, 56939270144, 642281037824, 2423854317568, 9177027411968, 34846713511936, 1459319692460032, 5568939824513024, 21297365878571008

Offset: 1

Author

Eric W. Weisstein, Jul 28 2017

Keywords

• nonn
• frac

Comments

For p > 3, if p is prime, then p^2 divides a(p). Conjecture: for n > 3, if n^2 divides a(n), then n is prime. Primes p such that p^3 diviedes a(p) are probably A088164. - Thomas Ordowski, Mar 30 2025

Examples

			First few terms are 0, 1, 6, 26, 100, 1096/3, 3920/3, 13936/3, 16544, 296256/5, ....
		

Links

• Eric Weisstein's World of Mathematics, Harary Index
• Eric Weisstein's World of Mathematics, Halved Cube Graph

Crossrefs

Cf. A000265, A088164, A290348 (denominators), A330718.

Programs

Mathematica

Table[-2^(n - 1) HarmonicNumber[n] - 2^(2 n - 1) Re[LerchPhi[2, 1, n + 1]], {n, 20}] // Numerator

Formula

a(n) = -2^(n-1)*HarmonicNumber(n)-2^(2*n-1)*Re(LerchPhi(2,1,n+1)).

For n > 1, A000265(a(n)) = A330718(n). - Thomas Ordowski, Mar 30 2025