cp's OEIS Frontend

A374918 Even numbers k such that lambda(sum of even divisors of k) = phi(sum of odd divisors of k) where lambda is the Carmichael function (A002322) and phi the Euler totient function (A000010).

%I A374918 #10 Aug 14 2024 19:43:11
%S A374918 2,6,10,12,14,18,26,28,34,36,42,50,52,62,72,74,84,100,106,112,122,124,
%T A374918 136,144,146,148,162,186,194,200,244,254,292,296,314,324,336,372,386,
%U A374918 388,424,434,482,488,496,508,554,576,578,584,626,628,656,674,688,762
%N A374918 Even numbers k such that lambda(sum of even divisors of k) = phi(sum of odd divisors of k) where lambda is the Carmichael function (A002322) and phi the Euler totient function (A000010).
%e A374918 a(18) = 100 because the divisors of 100 are {1, 2, 4, 5, 10, 20, 25, 50, 100} with lambda(2+4+10+20+50+100) = lambda(186) = 30 and phi(1+5+25) = phi(31) = 30.
%p A374918 with(numtheory):nn:=800:
%p A374918 for n from 2 by 2 to nn do:
%p A374918  d:=divisors(n):n0:=nops(d):s0:=0:s1:=0:
%p A374918     for i from 1 to n0 do:
%p A374918      if irem(d[i],2)=0
%p A374918       then
%p A374918         s0:=s0+d[i] else
%p A374918 s1:=s1+d[i]:
%p A374918      fi:
%p A374918     od:
%p A374918       if lambda(s0)=phi(s1) then
%p A374918 printf(`%d, `,n):else fi:
%p A374918    od:
%t A374918 Select[Range[2, 1000, 2], EulerPhi[DivisorSigma[1, #/2^IntegerExponent[#, 2]]] == CarmichaelLambda[2*DivisorSigma[1, #/2]] &] (* _Amiram Eldar_, Jul 23 2024 *)
%Y A374918 Cf. A000010, A000593, A002322, A074400.
%K A374918 nonn
%O A374918 1,1
%A A374918 _Michel Lagneau_, Jul 23 2024