A379264 -id:A379264 - cp's OEIS frontend

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

Massimo Kofler, Feb 25 2025

nonn

			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).

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

Intersection of A005100 and A000326.

Cf. A379264.

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

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

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

A382696 Centered pentagonal numbers that are abundant.

Original entry on oeis.org

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

Massimo Kofler, Apr 03 2025

nonn

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

			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).

Intersection of A005891 and A005101.

Cf. A379264.

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

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

A380892 Hexagonal numbers that are abundant.

Original entry on oeis.org

66, 120, 276, 378, 630, 780, 1128, 1326, 1540, 1770, 2016, 2556, 2850, 3160, 3486, 3828, 4560, 4950, 5778, 6216, 7140, 7626, 7875, 8646, 9180, 9730, 10296, 10878, 12090, 12720, 14028, 14706, 15400, 16110, 16836, 17955, 18336, 19110, 19900, 20706, 21528, 21945, 23220, 24090, 24976

Offset: 1

Massimo Kofler, Feb 07 2025

nonn

The least term that is coprime to 6 is a(30415179) = 9820742934657655. - Amiram Eldar, Feb 07 2025

			66 = 2*3*11 is a term since it is a hexagonal number and less than the sum of its proper divisors 78.
120 = 2^3*3*5 is a term since it is a hexagonal number and less than the sum of its proper divisors 240.
7875 = 3^2*5^3*7 is a term since it is a hexagonal number and less than the sum of its proper divisors 8349.

Intersection of A000384 and A005101.

Cf. A074315, A063734, A117794, A379264.

Select[Table[n*(2*n-1), {n, 1, 125}], DivisorSigma[-1, #] > 2 &] (* Amiram Eldar, Feb 07 2025 *)

select(x->sigma(x)>2*x, vector(150, k, k*(2*k-1))) \\ Michel Marcus, Feb 07 2025

cp's OEIS Frontend

A381488 Pentagonal numbers that are deficient.

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Magma

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A382696 Centered pentagonal numbers that are abundant.

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Maple

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A380892 Hexagonal numbers that are abundant.

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