A379264 Pentagonal numbers (or 5-gonal numbers, i.e., numbers of the form k*(3*k-1)/2) 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

1,1

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

Links

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

Example

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).

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 *)

Prog

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

Crossrefs

Intersection of A005101 and A000326.

Sequence in context: A088832 A366748 A198311 * A374977 A060930 A169725

Adjacent sequences: A379261 A379262 A379263 * A379265 A379266 A379267

Keyword

nonn

Author

Massimo Kofler, Dec 19 2024

Status

approved