Let q be a positive integer. Recently, Niu and Liu proved that, if n >=3D max{q, 1198 - q}, then the product (1(3)+ q(3))(2(3) + q(3)) ... (n(3) + q(3)) is not a powerful number. In this note, we prove (1) that, for any odd prime power l and n >=3D max{q, 11 - q}, the product (1(l) + q(l))(2(l) + q(l)) ... (n(l) + q(l)) is not a powerful number, and (2) that, for any positive odd integer l, there exists an integer N-q,N-l such that, for any positive integer n >=3D N-q,N-l, the product (1(l) + q(l))(2(l) + q(l)) ... (n(l) + q(l)) is not a powerful number. (c) 2017 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.

Quantum chemical calculations were performed on a series of novel divalent N-I compounds, CCC -> N+ <- CO (1), CCC -> N+ <- N-2 (2), CCC -> N+ <- PPh3 (3), CCC -> N+ <- C(NH2)(2) (4), CCC -> N+ <- NHCMe (5) CCC -> N+ <- N-methyl-4-pyridylidene (6) and CCC -> N+ <- Cyclopropenylidene (7), where CCC is a carbocyclic carbene (cyclohexa-2,5-diene-4-(diaminomethynyl)-1-ylidene). Complete optimization of 3D structures indicates that the chosen structures are the global minima on their respective potential energy surfaces (tautomeric alternatives are much less stable). The CCC -> N+ coordination bond length is in the range of 1.353-1.399 angstrom, supporting the C -> N coordination bond character. This is also supplemented by very low CCC -> N bond rotational barriers (> 8 kcal/mol). The CCC -> N <- L angles are in the range of 118 degrees-131 degrees, suggesting that there is no heteroallene-type character at the central nitrogen atom. Electron localization function, lone pair occupancy calculations and partial charge analysis indicate the presence of excess electron density at the N+ centre. The nucleophilicity of the designed compounds was further measured by calculating the proton affinity and complexation energies with various Lewis acids like BH3, AlCl3 and AuCl at the N+ centre. All these studies suggest the presence of divalent N-I character in the designed compounds 1-7.