A067880 -id:A067880 - 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S. W. Golomb, Equality among number-theoretic functions, Unpublished manuscript.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

A228519 Numbers n such that sigma(n) = sigma(n - phi(n)), where sigma(n) is the sum of divisors of n and phi(n) is the Euler totient function of n.

Original entry on oeis.org

9356, 52412, 110442, 160834, 220884, 266866, 289230, 321668, 420790, 441768, 533732, 556818, 578460, 643336, 731530, 841580, 883536, 1067464, 1113636, 1156920, 1286672, 1446150, 1463060, 1683160, 1767072, 2103950, 2134928, 2227272, 2313840, 2545888, 2573344, 2892300

Offset: 1

Paolo P. Lava, Jun 21 2016

Amiram Eldar, Table of n, a(n) for n = 1..1000

Cf. A000010, A000203, A051953, A067880.

with(numtheory); P:=proc(q) local n; for n from 1 to q do
if sigma(n)=sigma(n-phi(n)) then print(n); fi; od; end: P(10^9);

Select[Range[10^6], DivisorSigma[1, #] == DivisorSigma[1, # - EulerPhi@ #] &] (* Michael De Vlieger, Jun 21 2016 *)

sigma(9356- phi(9356)) = sigma(9356 - 4676) = 16380 = sigma(9356).

cp's OEIS Frontend

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

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