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

30, 42, 60, 66, 70, 74, 78, 82, 84, 86, 90, 94, 98, 102, 106, 110, 114, 118, 120, 122, 126, 130, 132, 134, 138, 140, 142, 146, 150, 154, 156, 158, 162, 165, 166, 168, 170, 174, 178, 180, 182, 186, 190, 194, 195, 198, 202, 204, 206, 210, 214, 218, 220, 222, 226

Offset

1,1

Comments

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).

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

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

The smallest odd term is 165.

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

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

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Example

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).

Mathematica

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

Crossrefs

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

Sequence in context: A090790 A090800 A114816 * A000977 A214195 A033992

Adjacent sequences: A299988 A299989 A299990 * A299992 A299993 A299994

Keyword

nonn

Author

Michael De Vlieger, Feb 25 2018

Status

approved