A236027 -id:A236027 - cp's OEIS frontend

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

Jaroslav Krizek, Jan 19 2014

nonn

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).

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

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

A236026 Sequence of numbers from A236025 such that A236025(n) > A236025(k) for all k < n.

Original entry on oeis.org

4, 6, 9, 10, 14, 15, 25, 26, 27, 33, 34, 49, 51, 55, 58, 62, 65, 69, 74, 77, 82, 86, 121, 169, 178, 183, 185, 194, 202, 206, 289, 361, 362, 365, 382, 386, 529, 538, 542, 543, 554, 562, 566, 573, 586, 591, 597, 614, 622, 841, 961, 974, 982, 998, 1006, 1018

Offset: 1

Jaroslav Krizek, Jan 21 2014

nonn

A236025 = composite numbers n sorted by increasing values of number 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.

Cf. A236020, A236021, A236022, A236023, A236024, A236025, A236027.

cp's OEIS Frontend

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.

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