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.

A341857 a(n) = psi(n^2)/n, psi = A002322.

This page as a plain text file.
%I A341857 #16 Mar 11 2024 07:33:51
%S A341857 1,1,2,1,4,1,6,2,6,2,10,1,12,3,4,4,16,3,18,1,2,5,22,2,20,6,18,3,28,2,
%T A341857 30,8,10,8,12,3,36,9,4,2,40,1,42,5,12,11,46,4,42,10,16,3,52,9,4,6,6,
%U A341857 14,58,1,60,15,6,16,12,5,66,4,22,6,70,6,72,18,20,9
%N A341857 a(n) = psi(n^2)/n, psi = A002322.
%C A341857 It is easy to show that n divides psi(n) for all n.
%C A341857 For k >= 2, n^k divides psi(n^(k+1)) if and only if n is not of the form 2*(p_1)^(e_1)*(p_2)^(e_2)*...*(p_m)^(e_m), where p_i are distinct odd primes not congruent to 1 modulo 2^k.
%C A341857 It seems that every positive integer occurs in this sequence. The first occurrence of each k is given by A341860.
%H A341857 Jianing Song, <a href="/A341857/b341857.txt">Table of n, a(n) for n = 1..10000</a>
%F A341857 For odd n > 1, a(2n) = a(n)/2.
%e A341857 psi(220^2) = psi(2^4 * 5^2 * 11^2) = lcm(psi(2^4), psi(5^2), psi(11^2)) = lcm(4, 20, 110) = 220, so a(220) = psi(220^2)/220 = 220/220 = 1.
%t A341857 Array[CarmichaelLambda[#^2]/# &, 100] (* _Paolo Xausa_, Mar 11 2024 *)
%o A341857 (PARI) a(n) = A002322(n^2)/n \\ See A002322 for its program
%Y A341857 Cf. A002322, A341860.
%Y A341857 Indices of 1 are given by A341858.
%K A341857 nonn
%O A341857 1,3
%A A341857 _Jianing Song_, Feb 21 2021