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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). 1
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 (list; graph; refs; listen; history; text; internal format)
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 * A137033 A045526 A164579

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

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Last modified November 21 11:01 EST 2018. Contains 317447 sequences. (Running on oeis4.)