A244666 -id:A244666 - cp's OEIS frontend

A244329 a(n) = floor(antisigma(n) / sigma(n)) = floor(A024816(n) / A000203(n)).

0, 0, 0, 0, 1, 0, 2, 1, 2, 2, 4, 1, 5, 3, 4, 3, 7, 3, 8, 4, 6, 6, 10, 4, 9, 7, 8, 6, 13, 5, 14, 7, 10, 10, 12, 6, 17, 11, 12, 8, 19, 8, 20, 10, 12, 14, 22, 8, 20, 12, 17, 13, 25, 11, 20, 12, 19, 18, 28, 9, 29, 19, 18, 15, 24, 14, 32, 17, 24, 16, 34, 12, 35, 23

Offset: 1

Jaroslav Krizek, Jul 08 2014

nonn

RECORD transform of a(n) is A140475 (union of number 1 and primes >= 5).
Sequence of numbers n such that a(n) = floor(antisigma(n) / n) = A046022.
Sequence of numbers n such that a(n) = a(n+1) = A244666.

			For n = 10; a(10) = floor(A024816(10) / A000203(10)) = floor(37 / 18) = 2.

Paolo Xausa, Table of n, a(n) for n = 1..10000

Cf. A000203, A000217, A024816, A046022, A140475, A244327, A244328, A244666.

[Floor(((n*(n+1)div 2)-SumOfDivisors(n)) div (SumOfDivisors(n))) : n in [1..1000]];

A244329[n_] := Floor[(n*(n + 1)/2 - #)/#] & [DivisorSigma[1, n]];
Array[A244329, 100] (* Paolo Xausa, Sep 01 2024 *)

a(n) = A244327(n) - A244328(n) for n >= 7.

A244327 a(n) = floor((n*(n+1)/2) / sigma(n)) = floor(A000217(n) / A000203(n)).

Original entry on oeis.org

1, 1, 1, 1, 2, 1, 3, 2, 3, 3, 5, 2, 6, 4, 5, 4, 8, 4, 9, 5, 7, 7, 11, 5, 10, 8, 9, 7, 14, 6, 15, 8, 11, 11, 13, 7, 18, 12, 13, 9, 20, 9, 21, 11, 13, 15, 23, 9, 21, 13, 18, 14, 26, 12, 21, 13, 20, 19, 29, 10, 30, 20, 19, 16, 25, 15, 33, 18, 25, 17, 35, 13, 36

Offset: 1

Jaroslav Krizek, Jul 08 2014

nonn

RECORD transform of a(n) is A140475 (union of number 1 and primes >= 5).

Sequence of numbers n such that a(n) = a(n+1) = A244666.

			For n = 10; a(10) = floor(A000217(10) / A000203(10)) = floor(55 / 18) = 3.

Alois P. Heinz, Table of n, a(n) for n = 1..20000

Cf. A000203, A000217, A024816, A244328, A244329, A244666.

[Floor((n*(n+1)div 2) div (SumOfDivisors(n))): n in [1..1000]];

a:= n-> floor(n*(n+1)/(2*numtheory[sigma](n))):
seq(a(n), n=1..100);  # Alois P. Heinz, Mar 28 2018

A244327[n_] := Floor[n*(n + 1)/(2*DivisorSigma[1, n])];
Array[A244327, 100] (* Paolo Xausa, Sep 01 2024 *)

a(n) = A244328(n) + A244329(n) for n >= 7.

cp's OEIS Frontend

A244329 a(n) = floor(antisigma(n) / sigma(n)) = floor(A024816(n) / A000203(n)).

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