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).

2, 6, 10, 12, 14, 18, 26, 28, 34, 36, 42, 50, 52, 62, 72, 74, 84, 100, 106, 112, 122, 124, 136, 144, 146, 148, 162, 186, 194, 200, 244, 254, 292, 296, 314, 324, 336, 372, 386, 388, 424, 434, 482, 488, 496, 508, 554, 576, 578, 584, 626, 628, 656, 674, 688, 762

Offset: 1

Author

Michel Lagneau, Jul 23 2024

Keywords

• nonn

Examples

			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.
		

Crossrefs

Cf. A000010, A000593, A002322, A074400.

Programs

Maple

with(numtheory):nn:=800:
for n from 2 by 2 to nn do:
 d:=divisors(n):n0:=nops(d):s0:=0:s1:=0:
    for i from 1 to n0 do:
     if irem(d[i],2)=0
      then
        s0:=s0+d[i] else
s1:=s1+d[i]:
     fi:
    od:
      if lambda(s0)=phi(s1) then
printf(`%d, `,n):else fi:
   od:

Mathematica

Select[Range[2, 1000, 2], EulerPhi[DivisorSigma[1, #/2^IntegerExponent[#, 2]]] == CarmichaelLambda[2*DivisorSigma[1, #/2]] &] (* Amiram Eldar, Jul 23 2024 *)