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Numbers n for which A243822(n) = A000005(n).
4

%I #11 Mar 02 2018 04:06:24

%S 34,38,46,50,54,58,62,105,249,267,268,284,291,292,303,309,316,321,324,

%T 327,332,339,356,363,381,385,388,393,404,411,412,417,428,436,447,452,

%U 453,455,471,484,489,500,501,507,508,519,537,543,573,579,591,595,597

%N Numbers n for which A243822(n) = A000005(n).

%C Indices of zeros in A299990, i.e., A010846(n) - 2*A000005(n) = 0.

%C Composite numbers m have nondivisors k in the cototient such that k | n^e with e > 1. These k appear in row n of A272618 and are enumerated by A243822(n). These nondivisors k are a kind of "regular" number along with divisors d of n; both are listed in row n of A162306 and are together enumerated by A045763(n). Divisors of n are listed in row n of A027750.

%C This sequence lists numbers that have an equal number of nondivisors k in the cototient of n as divisors d.

%C The smallest odd term is 105.

%H Michael De Vlieger, <a href="/A300155/b300155.txt">Table of n, a(n) for n = 1..10000</a>

%e 34 is the first term since it is the smallest number for which A243822(34) = A000005(34). For n = 34, there are 4 divisors {1, 2, 17, 34} and 4 nondivisors 1 <= m <= n such that m | n^e with e > 1: {4, 8, 16, 32}.

%t Select[Range@ 600, Function[n, Count[Range[n], _?(PowerMod[n, Floor@ Log2@ n, #] == 0 &)] == 2 DivisorSigma[0, n]]]

%Y Cf. A000005, A010846, A027750, A045763, A162306, A243822, A272618, A299990, A299991, A299992.

%K nonn

%O 1,1

%A _Michael De Vlieger_, Feb 26 2018