A256527 - OEIS

%I #34 Oct 11 2024 08:48:25

%S 1,1,15,3,14,6,6,42,30,42,168,210,210,420,840,20790,20790,9240,9240,

%T 83160,120120,3984120,5165160,43825320,26860680,43825320,1304863560,

%U 569729160,569729160,16522145640,18176198040,563462139240,1140028049160,3844800479520,1255683068640,65361608151840,65361608151840,65361608151840,413956851628320,1241870554884960,1241870554884960

%N a(n) is the least number k > 0 such that sigma(k) = phi(n*k).

%F For n >= 5, a(n) = A087979(n). - Conjectured by _Manfred Scheucher_, May 28 2015; proved by _Max Alekseyev_, Sep 29 2023

%e sigma(1)  = phi(1*1)  = 1;

%e sigma(1)  = phi(2*1)  = 1;

%e sigma(15) = phi(3*15) = 24;

%e sigma(3)  = phi(4*3)  = 4;

%e sigma(14) = phi(5*14) = 24;

%e sigma(6)  = phi(6*6)  = 12;

%e sigma(6)  = phi(7*6)  = 12;

%e sigma(42) = phi(8*42) = 96;

%e sigma(30) = phi(9*30) = 72; etc.

%p with(numtheory): P:=proc(q) local k, n;

%p for n from 1 to q do for k from 1 to q do

%p if sigma(k)=phi(k*n) then lprint(n,k); break; fi;

%p od; od; end: P(10^5);

%t Table[k = 1; While[DivisorSigma[1, k] != EulerPhi[n k], k++]; k, {n, 20}] (* _Michael De Vlieger_, May 28 2015 *)

%o (PARI) a(n) = {k=1; while(sigma(k) != eulerphi(n*k), k++); k;} \\ _Michel Marcus_, Apr 01 2015

%Y Except for a(4), same as A087979.

%Y Cf. A000010, A000203, A241762.

%K nonn

%O 1,3

%A _Paolo P. Lava_, Apr 01 2015

%E a(21)-a(23) from _Michel Marcus_, Apr 01 2015

%E a(24)-a(26) from _Jon E. Schoenfield_, Jun 28 2015

%E a(27)-a(35) from _Giovanni Resta_, May 24 2016

%E a(36)-a(41) from _Max Alekseyev_, Oct 10 2024