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

1,1

Links

Table of n, a(n) for n=1..56.

Example

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.

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 *)

Crossrefs

Cf. A000010, A000593, A002322, A074400.

Sequence in context: A095300 A097381 A264964 * A195064 A328926 A055743

Adjacent sequences: A374915 A374916 A374917 * A374919 A374920 A374921

Keyword

nonn

Author

Michel Lagneau, Jul 23 2024

Status

approved