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A172465 Numbers n such that phi(phi(n)) + sigma(sigma(n)) is an 8th power. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 24 17:57 EST 2021. Contains 340411 sequences. (Running on oeis4.)