A140790 Numbers n such that phi(n)*sigma(n)=phi(n-1)*sigma(n-1) (phi is the Euler totient function A000010 and sigma is the sum-of-divisors function A000203).

6, 56, 57, 124, 136, 148, 176, 305, 352, 645, 1016, 2465, 19305, 61132, 162525, 476672, 567645, 712725, 801945, 2435489, 3346400, 3885057, 4556000, 8085561, 8369361, 12516693, 22702120, 29628801, 83884032, 83994625, 84789248, 354812536, 860616296

Offset

1,1

Comments

Up to 5*10^12 only n=696004 satisfies the similar relation phi(n)/sigma(n)=phi(n-1)/sigma(n-1), or equivalently, phi(n)sigma(n-1)=phi(n-1)/sigma(n). - Giovanni Resta, Aug 05 2013

References

J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 136, pp 46, Ellipses, Paris 2008.

Links

Giovanni Resta, Table of n, a(n) for n = 1..52 (terms < 10^13)

K. Matthews, Factorizing n and calculating phi(n),omega(n),d(n),sigma(n) and mu(n)

Example

124 is in the sequence because phi(124)*sigma(124) = 60*224 = 13440 and phi(123)*sigma(123) = 80*168 = 13440, so that we indeed have phi(124)*sigma(124) = phi(123)*sigma(123).

Maple

lastv:= 0: A:= NULL:
for n from 1 to 10^7 do
  v:= numtheory:-phi(n)*numtheory:-sigma(n);
  if v = lastv then A:= A, n fi;
  lastv:= v;
od:
A; # Robert Israel, Feb 04 2018

Mathematica

Select[Range[10^7], EulerPhi[#]DivisorSigma[1, #] == EulerPhi[# - 1] DivisorSigma[1, # - 1] &] (* Vincenzo Librandi, Feb 05 2018 *)

Prog

(PARI) isok(n) = (eulerphi(n)*sigma(n) == eulerphi(n-1)*sigma(n-1)) \\ Michel Marcus, Jul 28 2013
(Magma) [n: n in [2..10^6] | (EulerPhi(n)*SumOfDivisors(n) eq EulerPhi(n-1)*SumOfDivisors(n-1))]; // Vincenzo Librandi, Feb 05 2018

Crossrefs

Sequence in context: A249672 A255853 A183594 * A335217 A335199 A137033

Adjacent sequences: A140787 A140788 A140789 * A140791 A140792 A140793

Keyword

nonn

Author

Lekraj Beedassy, Jul 14 2008

Extensions

a(29)-a(33) from Donovan Johnson, Jul 25 2011

Duplicated entry (19305) deleted by Giovanni Resta, Aug 05 2013

Status

approved