cp's OEIS Frontend

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.

A328558 Squares (A000290) that are not arithmetic numbers (A003601).

This page as a plain text file.
%I A328558 #12 Sep 08 2022 08:46:24
%S A328558 4,9,16,25,36,64,81,100,121,144,196,225,256,289,324,400,441,484,529,
%T A328558 576,625,676,729,784,841,900,1024,1089,1156,1225,1296,1444,1521,1600,
%U A328558 1681,1764,1936,2025,2116,2209,2304,2401,2500,2601,2704,2809,2916,3025,3136
%N A328558 Squares (A000290) that are not arithmetic numbers (A003601).
%C A328558 Numbers m such that the geometric mean of the divisors of m is an integer but the arithmetic mean of the divisors of m is not an integer.
%C A328558 Numbers m such that G(m) = sqrt(m) is an integer but A(m) = A000203(m) / A000005(m) is not an integer.
%C A328558 Corresponding values of G(m): 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, ...
%C A328558 Corresponding values of A(m): 7/3, 13/3, 31/5, 31/3, 91/9, 127/7, 121/5, 217/9, 133/3, 403/15, 133/3, 403/9, ...
%C A328558 Complement of A277793 with respect to A000290.
%t A328558 Select[Range[56]^2, !Divisible[DivisorSigma[1, #], DivisorSigma[0, #]] &] (* _Amiram Eldar_, Oct 20 2019 *)
%o A328558 (Magma) [m: m in [1..10^5] | not IsIntegral(SumOfDivisors(m) / NumberOfDivisors(m)) and IsIntegral(Sqrt(m))]
%o A328558 (PARI) isA328558(n) = (issquare(n)&&(sigma(n)%numdiv(n))); \\ _Antti Karttunen_, Oct 19 2019
%Y A328558 Cf. A000005, A000203, A000290, A003601, A277793, A328557, A328559.
%K A328558 nonn
%O A328558 1,1
%A A328558 _Jaroslav Krizek_, Oct 19 2019