A172465 Numbers n such that phi(phi(n)) + sigma(sigma(n)) is an 8th power.

42, 101, 6720, 9212, 226570, 276404, 288086, 299668, 339098, 392228, 412276, 423395, 530917, 535759, 559427, 564209, 666181, 2835284, 3592300, 3911744, 4080100, 5980673, 7230960, 8787900, 14960924, 17130550, 23324242, 27449729, 30437729, 33869141, 42073800

Offset

1,1

References

W. L. Glaisher, Number-Divisor Tables. British Assoc. Math. Tables, Vol. 8, Camb. Univ. Press, 1940, p. 64.

S. W. Golomb, Equality among number-theoretic functions, Abstract 882-11-16, Abstracts Amer. Math. Soc., 14 (1993), 415-416.

R. K. Guy, Unsolved Problems in Number Theory, B42.

Links

Hiroaki Yamanouchi, Table of n, a(n) for n = 1..267

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].

K. Ford, The distribution of totients, Electron. Res. Announc. Amer. Math. Soc. 4 (1998), 27-34.

Eric Weisstein's World of Mathematics, Carmichael's Totient Function conjecture

Example

phi(phi(9)) + sigma(sigma(9))= 1;
phi(phi(42)) + sigma(sigma(42))= 2^8 = 256;
phi(phi(101)) + sigma(sigma(101))= 2^8 = 256;
phi(phi(6720)) + sigma(sigma(6720))= 4^8 = 65536.

Maple

with(numtheory):for n from 1 to 2000000 do; if floor(( phi(phi(n)) + sigma(sigma(n)))^.125) = (phi(phi(n)) + sigma(sigma(n)))^.125 then print (n); fi ; od;

Prog

(PARI) isok(n) = ispower(eulerphi(eulerphi(n)) + sigma(sigma(n)), 8); \\ Michel Marcus, Sep 20 2014

Crossrefs

Cf. A000010, A002180, A032446, A058277.

Sequence in context: A177772 A169738 A063329 * A235109 A039470 A241049

Adjacent sequences: A172462 A172463 A172464 * A172466 A172467 A172468

Keyword

nonn

Author

Michel Lagneau, Feb 03 2010

Extensions

a(10) corrected and a(18)-a(31) added by Hiroaki Yamanouchi, Sep 19 2014

Status

approved