A076221 -id:A076221 - cp's OEIS frontend

A076222 Number of different values in n-th row of A076221.

1, 1, 1, 2, 2, 4, 4, 4, 4, 6, 6, 6, 6, 6, 8, 9, 9, 9, 9, 9, 8, 11, 11, 11, 11, 12, 11, 12, 12, 13, 13, 13, 15, 15, 16, 17, 17, 17, 17, 17, 17, 18, 18, 20, 20, 20, 20, 20, 19, 18, 19, 19, 19, 19, 24, 23, 24, 24, 24, 24, 24, 24, 24, 24, 21, 25, 25, 27, 27, 28, 28, 28, 28, 28, 28, 28

Offset: 1

Olivier Gérard

nonn

A076223 Minimum of n-th row of A076221.

Original entry on oeis.org

0, 1, 2, 2, 3, 2, 3, 3, 3, 3, 4, 4, 5, 5, 5, 5, 6, 6, 7, 7, 7, 7, 8, 8, 9, 9, 9, 9, 10, 8, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 11, 11, 12, 12, 12, 12, 13, 13, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 16, 16, 17, 17, 17, 17, 17, 17, 18, 18, 18, 18, 19, 19, 20, 20, 20, 20, 21, 21, 22, 22, 22

Offset: 1

Olivier Gérard

nonn

A076224 Counts of the minimum value in n-th row of A076221.

Original entry on oeis.org

1, 2, 3, 2, 2, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3

Offset: 1

Olivier Gérard

nonn

A076225 Counts of the maximum value in n-th row of A076221.

Original entry on oeis.org

1, 2, 3, 2, 3, 2, 3, 3, 3, 2, 3, 3, 4, 3, 3, 3, 4, 4, 5, 5, 5, 4, 5, 5, 5, 4, 4, 4, 5, 5, 6, 6, 6, 5, 5, 5, 6, 5, 5, 5, 6, 6, 7, 7, 7, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 7, 8, 8, 9, 8, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 11, 10, 10, 10, 10, 10, 11, 11, 11, 10, 11, 11, 11, 10, 10, 10, 11, 11, 11, 11, 11

Offset: 1

Olivier Gérard

nonn

Does a(n) always equal 1 + pi(n) - pi(n/2), where pi(x) is number of primes <= x? If so a(n) = A056171(n)+1. - Leroy Quet, Feb 06 2003.

This is true, because A076221(n,k) = n-1 iff either k = 1 or k is a prime with n/2 < k <= n. - Robert Israel, Aug 29 2016

Ethan Berkove and Michael Brilleslyper, Subgraphs of Coprime Graphs on Sets of Consecutive Integers, Integers (2022) Vol. 22, #A47, see p. 8.

Cf. A056171, A076221.

seq(1+numtheory:-pi(n) - numtheory:-pi(floor(n/2)),n=1..100); # Robert Israel, Aug 29 2016

A076226 Numbers m such that the largest of the most frequent values in m-th row of A076221 is different from m-1.

Original entry on oeis.org

10, 15, 16, 27

Offset: 1

Olivier Gérard

Is there any case larger than 26 (tested up to 300) ?

a(5), if it exists, exceeds 5000. - Sean A. Irvine, Mar 25 2025

Cf. A076221.

Definition corrected by Max Alekseyev, Dec 28 2024

A076235 Least of the least frequent values in rows of A076221.

Original entry on oeis.org

0, 1, 2, 2, 3, 2, 3, 3, 3, 3, 4, 5, 6, 5, 6, 6, 7, 7, 8, 9, 12, 10, 11, 11, 11, 11, 12, 15, 16, 8, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 11, 11, 12, 12, 12, 12, 13, 13, 28, 29, 29, 30, 31, 31, 15, 15, 15, 15, 16, 17, 18, 18, 18, 18, 19, 19, 20, 20, 20, 20, 21, 21, 22, 22, 22, 22, 22, 22

Offset: 1

Olivier Gérard

nonn

cp's OEIS Frontend

A076222 Number of different values in n-th row of A076221.

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A076223 Minimum of n-th row of A076221.

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A076224 Counts of the minimum value in n-th row of A076221.

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A076225 Counts of the maximum value in n-th row of A076221.

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A076226 Numbers m such that the largest of the most frequent values in m-th row of A076221 is different from m-1.

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A076235 Least of the least frequent values in rows of A076221.

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