A300155 Numbers n for which A243822(n) = A000005(n).

34, 38, 46, 50, 54, 58, 62, 105, 249, 267, 268, 284, 291, 292, 303, 309, 316, 321, 324, 327, 332, 339, 356, 363, 381, 385, 388, 393, 404, 411, 412, 417, 428, 436, 447, 452, 453, 455, 471, 484, 489, 500, 501, 507, 508, 519, 537, 543, 573, 579, 591, 595, 597

Offset

1,1

Comments

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

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.

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

The smallest odd term is 105.

Links

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

Example

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}.

Mathematica

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

Crossrefs

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

Sequence in context: A306119 A218006 A345510 * A250738 A281239 A295750

Adjacent sequences: A300152 A300153 A300154 * A300156 A300157 A300158

Keyword

nonn

Author

Michael De Vlieger, Feb 26 2018

Status

approved