A383025 Centered pentagonal numbers that are deficient.
1, 16, 31, 51, 76, 106, 141, 181, 226, 331, 391, 526, 601, 681, 766, 856, 951, 1051, 1156, 1381, 1501, 1756, 1891, 2031, 2326, 2481, 2641, 2806, 3151, 3331, 3706, 3901, 4101, 4306, 4516, 4731, 4951, 5176, 5641, 5881, 6376, 6631, 6891, 7156, 7426, 7701, 7981, 8266, 8851, 9151, 9766, 10081, 10401
Offset: 1
Keywords
Examples
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). 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). 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).
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
Programs
-
Maple
select(t -> numtheory:-sigma(t) < 2*t, [seq( (5*n^2+5*n+2)/2, n=0..100)]); # Robert Israel, May 13 2025
-
Mathematica
Select[Table[(5*n^2 + 5*n + 2)/2, {n, 0, 65}], DivisorSigma[-1, #] < 2 &] (* Amiram Eldar, Apr 13 2025 *)
Formula
a(n) == 1 (mod 5).
Comments