A381488 Pentagonal numbers that are deficient.

1, 5, 22, 35, 51, 92, 117, 145, 247, 287, 376, 425, 477, 590, 651, 715, 782, 925, 1001, 1162, 1247, 1335, 1426, 1617, 1717, 2035, 2147, 2501, 2625, 2882, 3015, 3151, 3577, 3725, 4187, 4347, 4845, 5017, 5551, 5735, 6112, 6305, 6501, 6902, 7107, 7315, 7526, 7957

Offset: 1

Author

Massimo Kofler, Feb 25 2025

Keywords

• nonn

Examples

			22 = 2*11 is the 4th pentagonal number and is a deficient number, since it is larger than the sum of its proper divisors (14).
117 = 3^2*13 is the 9th pentagonal number and is a deficient number, since it is larger than the sum of its proper divisors (65).
1001 = 7*11*13 is the 26th pentagonal number and is a deficient number, since it is larger than the sum of its proper divisors (343).
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..10046

Crossrefs

Intersection of A005100 and A000326.

Cf. A379264.

Programs

Magma

filtered := [n*(3*n-1) div 2 : n in [1..80] | &+ [1/d : d in Divisors(n*(3*n-1) div 2)] lt 2]; filtered; // Vincenzo Librandi, Mar 03 2025

Mathematica

Select[Table[n*(3*n-1)/2, {n, 1, 75}], DivisorSigma[-1, #] < 2 &] (* Amiram Eldar, Feb 25 2025 *)

PARI

select(x->sigma(x)<2*x, vector(100, k, k*(3*k-1)/2)) \\ Michel Marcus, Feb 25 2025