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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. 2
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 (list; graph; refs; listen; history; text; internal format)
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: A317857 A220827 A063015 * A284202 A275189 A091616

Adjacent sequences:  A282512 A282513 A282514 * A282516 A282517 A282518

KEYWORD

nonn

AUTHOR

Michel Lagneau, Feb 17 2017

STATUS

approved

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Last modified June 13 00:57 EDT 2021. Contains 344980 sequences. (Running on oeis4.)