A152000 a(n) is squarefree and such that for every prime p|a(n) and every prime q|p-1 then q|a(n) holds.

2, 6, 10, 30, 34, 42, 78, 102, 110, 114, 170, 210, 222, 330, 390, 410, 438, 510, 514, 546, 570, 582, 654, 714, 798, 930, 978, 1010, 1110, 1158, 1218, 1230, 1326, 1482, 1542, 1554, 1806, 1830, 1870, 1938, 2190, 2310, 2510, 2530

Offset: 1

Author

J. Luis, A. Yebra and J. Jimenez Urroz, Nov 19 2008

Keywords

• easy
• nonn

Comments

a(n) is a squarefree valid base.

Numbers m > 1 such that m equals A007947(A002618(m)). - Jon Maiga, Aug 08 2019

Links

• Jinyuan Wang, Table of n, a(n) for n = 1..10000
• J. Jimenez Urroz and J. Luis A.Yebra, On the equation a^x=x mod b^n, Journal of Integer Sequences, Vol. 12 (2009), Article 09.8.8.

Crossrefs

Cf. A002618, A007947, A151999.

Programs

Maple

A152000 := proc(n)
    if n = 1 then
        2;
    else
        for a from procname(n-1)+1 do
            if issqrfree(a) then
                pdvs := numtheory[factorset](a) ;
                aworks := true;
                for p in numtheory[factorset](a) do
                    for q in numtheory[factorset](p-1) do
                        if a mod q = 0 then
                            ;
                        else
                            aworks := false;
                        end if;
                    end do:
                end do:
                if aworks then
                    return a;
                end if;
            end if;
        end do:
    end if;
end proc: # R. J. Mathar, Jun 01 2013

Mathematica

rad[n_] := Times @@ (First@# & /@ FactorInteger@n);
Select[Range[2, 2530], # == rad[#*EulerPhi[#]] &] (* Jon Maiga, Aug 08 2019 *)

PARI

is(m) = factorback(factorint(m*eulerphi(m))[, 1]) == m && m > 1; \\ Jinyuan Wang, Aug 08 2019

Extensions

Corrected and extended by Michel Marcus, Jun 01 2013