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.

A324331 a(n) = (n-1)^2 - phi(n)*sigma(n), where phi is A000010 and sigma is A000203.

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%I A324331 #14 Dec 04 2023 01:32:35
%S A324331 -1,-2,-4,-5,-8,1,-12,-11,-14,9,-20,9,-24,25,4,-23,-32,55,-36,25,16,
%T A324331 81,-44,49,-44,121,-44,57,-56,265,-60,-47,64,225,4,133,-72,289,100,81,
%U A324331 -80,529,-84,169,64,441,-92,225,-90,541,196,249,-104,649,36,145,256,729,-116,793
%N A324331 a(n) = (n-1)^2 - phi(n)*sigma(n), where phi is A000010 and sigma is A000203.
%C A324331 For squarefree semiprimes n = p*q  a(n)=(p-q)^2 is a square. But the converse, a(n) is prime, can happen: see A324332.
%H A324331 Brian Alspach, <a href="https://doi.org/10.1016/0012-365X(82)90195-9">Research problems, Problem 18</a>, Discrete Math 40 (1982), page 126.
%F A324331 a(A006881(n)) = A176881(n)^2.
%F A324331 a(n) = A069249(n) - 2*n + 1. - _Amiram Eldar_, Dec 04 2023
%t A324331 Table[(n-1)^2 - EulerPhi[n]*DivisorSigma[1, n], {n, 1, 60}] (* _Vaclav Kotesovec_, Feb 23 2019 *)
%o A324331 (PARI) a(n) = (n-1)^2 - eulerphi(n)*sigma(n);
%Y A324331 Cf. A000010, A000203, A006881, A069249, A176881.
%Y A324331 Cf. A324332, A324333, A324334.
%K A324331 sign,easy
%O A324331 1,2
%A A324331 _Michel Marcus_, Feb 23 2019