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A299991 Numbers n for which A243822(n) > A000005(n). 6

%I

%S 30,42,60,66,70,74,78,82,84,86,90,94,98,102,106,110,114,118,120,122,

%T 126,130,132,134,138,140,142,146,150,154,156,158,162,165,166,168,170,

%U 174,178,180,182,186,190,194,195,198,202,204,206,210,214,218,220,222,226

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

%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 A010846(n).

%C This sequence lists numbers that have more nondivisors k in the cototient of n than divisors d.

%C This sequence contains all n for which A299990(n) is positive.

%C The smallest odd term is 165.

%C For m >= 3, A002110(m) is in a(n).

%C For m >= 9, A244052(m) is in a(n).

%H Michael De Vlieger, <a href="/A299991/b299991.txt">Table of n, a(n) for n = 1..10000</a>

%e 30 is the first term since it is the smallest number for which A243822(n) > A000005(n), alternatively, for which A010846(n) > 2*A000005(n).

%t Select[Range@ 226, Function[n, Count[Range[n], _?(PowerMod[n, Floor@ Log2@ n, #] == 0 &)] > 2 DivisorSigma[0, n]]]

%Y Cf. A000005, A002110, A010846, A162306, A243822, A272618, A299990.

%K nonn

%O 1,1

%A _Michael De Vlieger_, Feb 25 2018

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Last modified August 8 06:27 EDT 2020. Contains 336290 sequences. (Running on oeis4.)