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

Author

Jaroslav Krizek, Jan 18 2014

Keywords

• nonn

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.