A006872 Numbers k such that phi(k) = phi(sigma(k)). (Formerly M2984)

1, 3, 15, 26, 39, 45, 74, 104, 111, 117, 122, 146, 175, 183, 195, 219, 296, 314, 333, 357, 386, 471, 488, 549, 554, 555, 579, 584, 585, 608, 626, 646, 657, 794, 831, 842, 914, 915, 939, 962, 1071, 1082, 1095, 1191, 1226, 1256, 1263, 1292, 1322, 1346

Offset

1,2

References

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.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000 (terms 1..1000 from T. D. Noe, terms 1001..12394 from Marius A. Burtea)

S. W. Golomb, Letter to N. J. A. Sloane, Oct. 1992

S. W. Golomb, Equality among number-theoretic functions, Unpublished manuscript. (Annotated scanned copy)

Mathematica

Select[Range@ 1350, EulerPhi@ # == EulerPhi@ DivisorSigma[1, #] &] (* Michael De Vlieger, Jan 01 2019 *)

Prog

(PARI) lista(nn) = {for (i=1, nn, if (eulerphi(i)==eulerphi(sigma(i)), print1(i, ", ")); ); } \\ Michel Marcus, May 25 2013
(Haskell)
a006872 n = a006872_list !! (n-1)
a006872_list = filter (\x -> a000010' x == a000010' (a000203' x)) [1..]
-- Reinhard Zumkeller, Jul 14 2015
(Magma) [n:n in [1..2000]| EulerPhi(SumOfDivisors(n)) eq EulerPhi(n)]; // Marius A. Burtea, Jan 01 2019

Crossrefs

Cf. A000010, A000203, A062401, A353637 (characteristic function).

Positions of zeros in A353636.

Setwise difference of A353684 and A353683, and also of A353685 and A353686.

Intersection of A353684 and A353685.

Subsequences: A260021, A353634, A353635, A353679 (odd terms).

Cf. also A033631, A033632, A067880, A137815, A260020.

Sequence in context: A046283 A160991 A328387 * A027179 A110703 A121250

Adjacent sequences: A006869 A006870 A006871 * A006873 A006874 A006875

Keyword

nonn

Author

Jeffrey Shallit, N. J. A. Sloane

Extensions

More terms from Jud McCranie

Status

approved