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A172466
Numbers n such that sigma(sigma(phi(n))) = sigma(sigma(n)).
1
1, 45, 65, 87, 117, 362, 1053, 1257, 1282, 1539, 1798, 2962, 2966, 3478, 5002, 5242, 5932, 9272, 9374, 9477, 10550, 10732, 12975, 13526, 14427, 20025, 21782, 21982, 21986, 22436, 23386, 23728, 25978, 25994, 27764, 32146, 35306, 35414, 36412, 38372, 38675
OFFSET
1,2
REFERENCES
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 840.
T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1976, page 38
LINKS
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
C. K. Caldwell, The Prime Glossary, sigma function
EXAMPLE
phi(45) = 24; sigma(phi(45)) = sigma(24) = 60; sigma(sigma(phi(45))) = sigma(60) = 168; sigma(45) = 78; sigma(sigma(45)) = sigma(78) = 168.
MAPLE
with(numtheory): for n from 1 to 1000000 do; if sigma(sigma(phi(n)))= sigma(sigma(n)) then print(n); fi ; od;
MATHEMATICA
Select[Range[40000], DivisorSigma[1, DivisorSigma[1, EulerPhi[#]]] == DivisorSigma[ 1, DivisorSigma[ 1, #]]&] (* Harvey P. Dale, Nov 22 2016 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Lagneau, Feb 03 2010
STATUS
approved