A241762 - OEIS

%I #28 Oct 01 2023 02:28:19

%S 1,2,45,12,70,36,42,336,270,420,1848,2520,2730,5880,12600,332640,

%T 353430,166320,175560,1663200,2522520,87650640,118798680,1051807680,

%U 671517000,1139458320,35231316120,15952416480,16522145640,495664369200,563462139240,18030788455680,37620925622280,130723216303680,43948907402400

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

%F a(n) = n * A256527(n). - _Max Alekseyev_, Sep 29 2023

%e For n=11, the least number is 1848. In fact, sigma(1848/11) = phi(1848) = 480.

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

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

%p if sigma(n/k)=phi(n) then print(n); break; fi;

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

%o (PARI) for(k=1,29,n=0;for(i=1,2^64,if(sigma(i)==eulerphi(i*k),n=i*k;break)); print(k,"  ",n)) \\ _Dana Jacobsen_, May 02 2014

%o (Perl) use Math::Prime::Util qw/:all/; for $k (1..29) { $i=1; $i++ while divisor_sum($i) != euler_phi($i*$k); say "$k  ",$i*$k; } # _Dana Jacobsen_, May 02 2014

%Y Cf. A000010, A000203, A087979.

%K nonn

%O 1,2

%A _Paolo P. Lava_, Apr 28 2014

%E a(22)-a(26) from _Giovanni Resta_, Apr 29 2014

%E a(27)-a(29) from _Dana Jacobsen_, May 02 2014

%E a(30)-a(35) from _Max Alekseyev_, Sep 29 2023