cp's OEIS Frontend

A256545 Composite numbers k such that k*phi(k) is in A002378.

%I A256545 #20 Dec 01 2020 02:52:53
%S A256545 6,30,434,510,616,912,1640,2989,3003,5934,7280,8600,10726,12700,13825,
%T A256545 14288,18699,19389,54153,59394,59906,70563,72816,116052,117964,121954,
%U A256545 131070,134212,140752,177000,206514,210728,274023,319522,418610,437736,456666
%N A256545 Composite numbers k such that k*phi(k) is in A002378.
%C A256545 Composite k such that 4*A002618(k)+1 is a square.
%C A256545 For all primes p, 4*A002618(p) + 1 = (2*p-1)^2.
%C A256545 The only semiprime < 10^7 in the sequence is 6.
%C A256545 k = 2*p with p prime is in the sequence if 2*p-1 is in A001653. However, the only such p < 10^3000 is 3.
%C A256545 Similarly, k = 3*p with p prime is in the sequence if 2*p-1 is in A080806. However, the only such p < 10^3000 is 2.
%H A256545 Amiram Eldar, <a href="/A256545/b256545.txt">Table of n, a(n) for n = 1..258</a> (terms below 10^11; terms 1..62 from Robert Israel)
%e A256545 a(1) = 6 is in the sequence because 6*phi(6) = 12 = 4*3.
%p A256545 select(n -> not isprime(n) and issqr(1+4*n*numtheory:-phi(n)), [$1..10^6]);
%t A256545 Select[Range[10^6],!PrimeQ[#]&&IntegerQ[Sqrt[4*#*EulerPhi[#]+1]]&] (* _Ivan N. Ianakiev_, Apr 02 2015 *)
%o A256545 (PARI) lista(nn) = {forcomposite (n=1, nn, if (ispolygonal(n*eulerphi(n)/2, 3), print1(n ", ")););} \\ _Michel Marcus_, Apr 02 2015
%Y A256545 Cf. A000010, A001653, A002378, A002618, A080806.
%K A256545 nonn
%O A256545 1,1
%A A256545 _Robert Israel_, Apr 01 2015