A282515 Numbers m such that phi(sum of the divisors of m) = phi(sum of the distinct prime divisors of m) where phi is the Euler totient function.

3, 6, 10, 22, 34, 142, 178, 214, 382, 862, 1402, 2302, 5182, 9098, 15398, 17398, 21178, 23602, 279934, 289558, 296734, 368062, 900754, 944782, 1079374, 1563442, 1572862, 1990654, 2116342, 2505886, 2584882, 2691574, 2858698, 2883058, 3351214, 3909046

Offset

1,1

Comments

Or numbers m such that A000010(A000203(m)) = A000010(A008472(m)).

For n > 1, we observe that a(n) is semiprime of the form a(n) = 2p with p = 3, 5, 11, 17, 71, 89, 107, 191, 431, 701, 1151, 2591, 4549, 7699, 8699, 10589, 11801, ... Except for the primes 3, 4549 and 7699 in the first 35 terms (from 6 until 3909046), the primes p are of the form 6k - 1.

Links

Amiram Eldar, Table of n, a(n) for n = 1..289 (terms below 10^10)

Example

34 is in the sequence because A000010(A000203(34)) = A000010(54) = 18 and A000010(A008472(34)) = A000010(19) = 18.

Maple

with(numtheory):
for n from 2 to 200000 do:
x:=divisors(n):n0:=nops(x):y:=factorset(n):n1:=nops(y):
   s0:=sum(‘x[i]’, ‘i’=1..n0):s1:=sum(‘y[i]’, ‘i’=1..n1):
    if phi(s1)=phi(s0)
     then
       print(n):
       else
     fi:
od:

Mathematica

Select[Range[10^6], EulerPhi@ DivisorSigma[1, #] == EulerPhi[Total@ FactorInteger[#][[All, 1]]] &] (* Michael De Vlieger, Feb 17 2017 *)

Prog

(PARI) isok(n) = my(f=factor(n)); eulerphi(sigma(n)) == eulerphi(vecsum(f[, 1])); \\ Michel Marcus, Feb 25 2017

Crossrefs

Cf. A000010, A000203, A008472, A062401.

Sequence in context: A220827 A063015 A362909 * A284202 A275189 A091616

Adjacent sequences: A282512 A282513 A282514 * A282516 A282517 A282518

Keyword

nonn

Author

Michel Lagneau, Feb 17 2017

Status

approved