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 A327295 #62 Dec 11 2019 09:51:29
%S A327295 4,12,16,48,80,112,132,208,240,1104,1456,1892,2128,4144,5852,12208,
%T A327295 17292,18544,21424,25456,30160,45904,78736,97552,106384,138864,153596,
%U A327295 154960,160528,289772,311920,321904,399212,430652,545584,750064,770704,979916,1037040,1058512
%N A327295 Numbers k such that e(k) > 1 and k == e(k) (mod lambda(k)), where e(k) = A051903(k) is the maximal exponent in prime factorization of k.
%C A327295 The condition e(k) > 1 excludes primes and Carmichael numbers.
%C A327295 Numbers n such that e(k) > 1 and b^k == b^e(k) (mod k) for all b.
%C A327295 These are numbers k such that A276976(k) = e(k) > 1.
%C A327295 Are there infinitely many such numbers? Are all such numbers even?
%C A327295 A number k is a term if and only if k is e(k)-Knödel number with e(k) > 1. So they may have the name nonsquarefree e(k)-Knodel numbers k.
%C A327295 It seems that if k is in this sequence, then e(k) = A007814(k) and k/2^e(k) is squarefree.
%C A327295 Conjecture: there are no composite numbers m > 4 such that m == e(m) (mod phi(m)). By Lehmer's totient conjecture, there are no such squarefree numbers.
%C A327295 Problem: are there odd numbers n such that e(n) > 1 and n == e(n) (mod ord_{n}(2)), where ord_{n}(2) = A002326((n-1)/2)? These are odd numbers n such that 2^n == 2^e(n) (mod n) with e(n) > 1.
%C A327295 Numbers k for which A051903(k) > 1 and A219175(k) = A329885(k). - _Antti Karttunen_, Dec 11 2019
%H A327295 Amiram Eldar, <a href="/A327295/b327295.txt">Table of n, a(n) for n = 1..500</a>
%e A327295 The number 4 = 2^2 is a term, because e(4) = A051903(4) = 2 > 1 and 4 == 2 (mod lambda(4)), where lambda(4) = A002322(4) = 2.
%t A327295 Select[Range[10^5], (e = Max @@ Last /@ FactorInteger[#]) > 1 && Divisible[# -e, CarmichaelLambda[#]] &] (* _Amiram Eldar_, Dec 05 2019 *)
%o A327295 (PARI) isok(n) = ! issquarefree(n) && (Mod(n, lcm(znstar(n)[2])) == vecmax(factor(n)[, 2])); \\ _Michel Marcus_, Dec 05 2019
%Y A327295 Cf. A000010, A002322, A002326, A002997, A050990, A050992, A051903, A068494, A219175, A270096, A276976, A324050, A327979, A329885.
%Y A327295 A proper subset of A013929.
%K A327295 nonn
%O A327295 1,1
%A A327295 _Thomas Ordowski_, Dec 05 2019
%E A327295 More terms from _Amiram Eldar_, Dec 05 2019