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

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

Author

Jeffrey Shallit, N. J. A. Sloane

Keywords

• nonn

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• S. W. Golomb, Equality among number-theoretic functions, Unpublished manuscript.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)

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.

Programs

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

Mathematica

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

PARI

lista(nn) = {for (i=1, nn, if (eulerphi(i)==eulerphi(sigma(i)), print1(i, ", ")););} \\ Michel Marcus, May 25 2013

Extensions

More terms from Jud McCranie