A172466 Numbers n such that sigma(sigma(phi(n))) = sigma(sigma(n)).

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

Donovan Johnson, Table of n, a(n) for n = 1..1000

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

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

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

Cf. A001157, A001158, A001160, A001065.

Sequence in context: A140278 A046426 A056776 * A038494 A026043 A372291

Adjacent sequences: A172463 A172464 A172465 * A172467 A172468 A172469

Keyword

nonn

Author

Michel Lagneau, Feb 03 2010

Status

approved