A379264 Pentagonal numbers that are abundant.

12, 70, 176, 210, 330, 532, 852, 1080, 1520, 1820, 1926, 2262, 2380, 2752, 3290, 3432, 3876, 4030, 4510, 4676, 5192, 5370, 5922, 6700, 7740, 8400, 9560, 10542, 11310, 12376, 12650, 13776, 14652, 14950, 17120, 17442, 18426, 18760, 19780, 20475, 21540, 22632, 25676, 26070, 27270, 27676, 28912, 29330, 31032

Offset: 1

Author

Massimo Kofler, Dec 19 2024

Keywords

• nonn

Comments

If k is even and k/2 or 3*k-1 is nondeficient, or k is odd and k or (3*k-1)/2 is nondeficient, then A000326(k) is a term. - Robert Israel, Jan 29 2025

The least term that is coprime to 6 is a(2426895) = 81026029008925. - Amiram Eldar, Feb 07 2025

Examples

			12=2^2*3 is the 3rd pentagonal number and it is smaller than the sum of its proper divisors (1+2+3+4+6=16).
70=2*5*7 is the 7th pentagonal number and it is smaller than the sum of its proper divisors (1+2+5+7+10+14+35=74).
176=2^4*11 is the 11th pentagonal number and it is smaller than the sum of its proper divisors (1+2+4+8+11+16+22+44+88=196).
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Intersection of A005101 and A000326.

Programs

Maple

select(t -> numtheory:-sigma(t) > 2*t, [seq(k*(3*k-1)/2,k=1..300)]); # Robert Israel, Jan 28 2025

Mathematica

Select[Table[k*(3*k-1)/2, {k, 1, 150}], DivisorSigma[-1, #] > 2 &] (* Amiram Eldar, Dec 19 2024 *)

PARI

select(x->(sigma(x)>2*x), vector(150, k, k*(3*k-1)/2)) \\ Michel Marcus, Dec 20 2024