A353634 -id:A353634 - cp's OEIS frontend

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

Jeffrey Shallit, N. J. A. Sloane

nonn

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).

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S. W. Golomb, Equality among number-theoretic functions, Unpublished manuscript.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

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.

a006872 n = a006872_list !! (n-1)
a006872_list = filter (\x -> a000010' x == a000010' (a000203' x)) [1..]
-- Reinhard Zumkeller, Jul 14 2015

[n:n in [1..2000]| EulerPhi(SumOfDivisors(n)) eq EulerPhi(n)]; // Marius A. Burtea, Jan 01 2019

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

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

More terms from Jud McCranie

A353635 Numbers k such that phi(k) = phi(sigma(k)) and A003958(k) = A003958(sigma(k)).

Original entry on oeis.org

1, 26, 74, 122, 146, 314, 386, 554, 626, 794, 842, 914, 1082, 1226, 1322, 1346, 1466, 1514, 1754, 1994, 2186, 2306, 2402, 2426, 2474, 2642, 2762, 2906, 3242, 3314, 3506, 3746, 3866, 3986, 4034, 4274, 4682, 4946, 5114, 5186, 5594, 5714, 5834, 6122, 6434, 6506, 6626, 7034, 7466, 8042, 8114, 8354, 8522, 8546, 8714, 8882

Offset: 1

Antti Karttunen, May 04 2022

nonn

Question 1: Are there any odd terms after the initial 1?

Interestingly, most of the terms seem to belong to a set where the abundancy index (ratio sigma(n)/n) converges towards 3/2. But there are exceptions, see A353634 for example.

Intersection of A006872 and A351446. A353634 lists the nondeficient terms.

Cf. A000010, A000203, A003958, A062401, A351440, A351442.

A003958(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1]--); factorback(f); };
isA353635(n) = { my(s=sigma(n)); ((eulerphi(s)==eulerphi(n)) && (A003958(s)==A003958(n))); };

cp's OEIS Frontend

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

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