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

1,2

Links

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

Example

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).

Mathematica

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

Prog

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

Crossrefs

Intersection of A005100 and A000326.

Cf. A379264.

Sequence in context: A288676 A085101 A350120 * A290510 A184724 A082005

Adjacent sequences: A381485 A381486 A381487 * A381489 A381490 A381491

Keyword

nonn,new

Author

Massimo Kofler, Feb 25 2025

Status

approved