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 A383025 #15 May 14 2025 01:09:54
%S A383025 1,16,31,51,76,106,141,181,226,331,391,526,601,681,766,856,951,1051,
%T A383025 1156,1381,1501,1756,1891,2031,2326,2481,2641,2806,3151,3331,3706,
%U A383025 3901,4101,4306,4516,4731,4951,5176,5641,5881,6376,6631,6891,7156,7426,7701,7981,8266,8851,9151,9766,10081,10401
%N A383025 Centered pentagonal numbers that are deficient.
%C A383025 The centered pentagonal numbers that are prime are terms (see A145838).
%H A383025 Robert Israel, <a href="/A383025/b383025.txt">Table of n, a(n) for n = 1..10000</a>
%F A383025 a(n) == 1 (mod 5).
%e A383025 16 = 2^4 is a term since it is the 3rd centered pentagonal number and larger than the sum of its proper divisors (1+2+4+8=15).
%e A383025 51 = 3*17 is a term since it is the 5th centered pentagonal number and larger than the sum of its proper divisors (1+3+17=21).
%e A383025 76 = 2^2*19 is a term since it is the 6th centered pentagonal number and larger than the sum of its proper divisors (1+2+4+19+38=64).
%p A383025 select(t -> numtheory:-sigma(t) < 2*t, [seq( (5*n^2+5*n+2)/2, n=0..100)]); # _Robert Israel_, May 13 2025
%t A383025 Select[Table[(5*n^2 + 5*n + 2)/2, {n, 0, 65}], DivisorSigma[-1, #] < 2 &] (* _Amiram Eldar_, Apr 13 2025 *)
%Y A383025 Intersection of A005891 and A005100.
%Y A383025 Cf. A145838, A381488, A382696.
%K A383025 nonn
%O A383025 1,2
%A A383025 _Massimo Kofler_, Apr 13 2025