A236022 Composite numbers n sorted by increasing values of gamma(n) = log_2(n+1) - log_tau(n) (sigma(n)), where sigma(n) = A000203(n) = the sum of divisors of n and tau(n) = A000005(n) = the number of divisors of n.

4, 9, 6, 8, 10, 25, 14, 15, 12, 22, 16, 21, 49, 26, 27, 18, 34, 33, 20, 38, 35, 39, 46, 121, 28, 51, 58, 169, 24, 62, 57, 55, 32, 74, 69, 65, 82, 30, 86, 289, 94, 77, 87, 44, 85, 93, 106, 361, 45, 91, 95, 50, 118, 36, 52, 122, 111, 40, 42, 134, 123, 115, 142

Offset

1,1

Comments

The number gamma(n) = log_2(n+1) - log_tau(n) (sigma(n)) is called the gamma-deviation from primality of the number n; gamma(p) = 0 for p = prime.

Conjecture: every natural number n has a unique value of gamma(n).

For number 4; gamma(4) = log_2 (4+1) - log_tau(4) (sigma(4)) = log_2 (5) - log_3 (7) = 0,5506843457… = A236023 (minimal value of function gamma(n)).

See A234516, A234520 and A236025 for definitions of functions alpha(n), beta(n) and delta(n).

See A236024 - sequence of numbers from a(n) such that a(n) > a(k) for all k < n.

Links

Jaroslav Krizek, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A236020, A236021, A236023, A236024, A236025, A236026.

Sequence in context: A200383 A199513 A360004 * A075635 A362213 A094243

Adjacent sequences: A236019 A236020 A236021 * A236023 A236024 A236025

Keyword

nonn

Author

Jaroslav Krizek, Jan 18 2014

Status

approved