A382696 Centered pentagonal numbers that are abundant.

276, 456, 1266, 1626, 2176, 2976, 3516, 5406, 6126, 8556, 9456, 12426, 13506, 17016, 18276, 22326, 23766, 28356, 29976, 35106, 36906, 39376, 42576, 44556, 50766, 52926, 59676, 62016, 69306, 71826, 79656, 82356, 89776, 90726, 93606, 94576, 102516, 105576, 115026, 118266, 128256, 131676, 142206, 145806

Offset: 1

Author

Massimo Kofler, Apr 03 2025

Keywords

• nonn

Comments

The sequence is infinite, e.g. A005891(n) is a term when 1 < n == 1 or 10 (mod 12). - Robert Israel, Apr 06 2025

Examples

			276 = 2^2*3*23 is a term since it is a centered pentagonal number and less than the sum of its proper divisors (1+2+3+4+6+12+23+46+69+92+138=396).
456 = 2^3*3*19 is a term since it is a centered pentagonal number and less than the sum of its proper divisors  (1+2+3+4+6+8+12+19+24+38+ 57+ 76+114+152+228=744).
		

Crossrefs

Intersection of A005891 and A005101.

Cf. A379264.

Programs

Maple

select(t -> numtheory:-sigma(t) > 2*t, [seq((5*n^2+5*n+2)/2, n=1..500)]); # Robert Israel, Apr 06 2025

Mathematica

Select[Table[(5*n^2 + 5*n + 2)/2, {n, 1, 250}], DivisorSigma[-1, #] > 2 &] (* Amiram Eldar, Apr 03 2025 *)