A236025 Composite numbers n sorted by increasing values of delta(n) = (n+1)^(1/2) - sigma(n)^(1/tau(n)), where sigma(n) = A000203(n) = the sum of divisors of n and tau(n) = A000005(n) = the number of divisors of n.

4, 6, 9, 8, 10, 14, 15, 12, 25, 16, 21, 22, 18, 26, 20, 27, 33, 34, 49, 24, 35, 28, 38, 39, 32, 30, 46, 51, 36, 55, 58, 44, 57, 40, 45, 42, 62, 50, 65, 52, 69, 48, 74, 54, 77, 56, 82, 63, 86, 121, 85, 64, 68, 87, 60, 94, 66, 93, 91, 81, 75, 95, 76, 70, 106, 78

Offset

1,1

Comments

The number delta(n) = (n+1)^(1/2) - sigma(n)^(1/tau(n)) is called the delta-deviation from primality of the number n; delta(p) = 0 for p = prime.

For number 4; delta(4) = (4+1)^(1/2) - sigma(4)^(1/tau(4)) = 5^(1/2) - 7^(1/3) = 0.32313679472... = A236027 (minimal value of function delta(n)).

See A234516, A234520 and A236022 for definitions of functions alpha(n), beta(n) and gamma(n).

See A236026 - sequence of numbers a(n) such that a(n) > a(k) for all k < n.

Conjecture: Every natural number n has a unique value of number delta(n).

Links

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

Crossrefs

Cf. A236020, A236021, A236022, A236023, A236024, A236026, A236027.

Sequence in context: A180853 A085088 A073870 * A377181 A218036 A236536

Adjacent sequences: A236022 A236023 A236024 * A236026 A236027 A236028

Keyword

nonn

Author

Jaroslav Krizek, Jan 19 2014

Status

approved