This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A379264 #22 Apr 04 2025 22:30:05
%S A379264 12,70,176,210,330,532,852,1080,1520,1820,1926,2262,2380,2752,3290,
%T A379264 3432,3876,4030,4510,4676,5192,5370,5922,6700,7740,8400,9560,10542,
%U A379264 11310,12376,12650,13776,14652,14950,17120,17442,18426,18760,19780,20475,21540,22632,25676,26070,27270,27676,28912,29330,31032
%N A379264 Pentagonal numbers that are abundant.
%C A379264 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
%C A379264 The least term that is coprime to 6 is a(2426895) = 81026029008925. - _Amiram Eldar_, Feb 07 2025
%H A379264 Robert Israel, <a href="/A379264/b379264.txt">Table of n, a(n) for n = 1..10000</a>
%e A379264 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).
%e A379264 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).
%e A379264 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).
%p A379264 select(t -> numtheory:-sigma(t) > 2*t, [seq(k*(3*k-1)/2,k=1..300)]); # _Robert Israel_, Jan 28 2025
%t A379264 Select[Table[k*(3*k-1)/2, {k, 1, 150}], DivisorSigma[-1, #] > 2 &] (* _Amiram Eldar_, Dec 19 2024 *)
%o A379264 (PARI) select(x->(sigma(x)>2*x), vector(150, k, k*(3*k-1)/2)) \\ _Michel Marcus_, Dec 20 2024
%Y A379264 Intersection of A005101 and A000326.
%K A379264 nonn
%O A379264 1,1
%A A379264 _Massimo Kofler_, Dec 19 2024