A375037 - OEIS

A375037

Irregular triangle read by rows T(n,k), n >= 1, k >= 1, in which row n lists the divisors of n but every middle divisor is replaced with zero.

0, 0, 2, 1, 3, 1, 0, 4, 1, 5, 1, 0, 0, 6, 1, 7, 1, 0, 4, 8, 1, 0, 9, 1, 2, 5, 10, 1, 11, 1, 2, 0, 0, 6, 12, 1, 13, 1, 2, 7, 14, 1, 0, 0, 15, 1, 2, 0, 8, 16, 1, 17, 1, 2, 0, 6, 9, 18, 1, 19, 1, 2, 0, 0, 10, 20, 1, 3, 7, 21, 1, 2, 11, 22, 1, 23, 1, 2, 3, 0, 0, 8, 12, 24

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OFFSET

1,3

COMMENTS

The nonzero terms in row n are the nonmiddle divisors of n.

The nonmiddle divisors of n are here the divisors of n that are not in the half-open interval [sqrt(n/2), sqrt(n*2)).

LINKS

Table of n, a(n) for n=1..84.

EXAMPLE

Triangle begins:

0, 2;

1, 3;

1, 0, 4;

1, 5;

1, 0, 0, 6;

1, 7;

1, 0, 4, 8;

1, 0, 9;

1, 2, 5, 10;

1, 11;

1, 2, 0, 0, 6, 12;

...

For n = 12 the divisors of 12 are [1, 2, 3, 4, 6, 12] and the middle divisors are [3, 4], but here the middle divisors are replaced with zeros, so the 12th row of the triangle is [1, 2, 0, 0, 6, 12].

MATHEMATICA

row[n_] := Divisors[n] /. {x_?(Sqrt[n/2] <= # < Sqrt[2*n] &) -> 0}; Table[row[n], {n, 1, 24}] // Flatten (* Amiram Eldar, Jul 29 2024 *)

CROSSREFS

Row sums give A302433.

Nonzero terms give A375038.

Row lengths give A000005.

The number of zeros in row n is A067742(n).

The number of nonzero terms in row n is A067743(n).

Cf. A000005, A027750, A067742, A299761, A303297.

Sequence in context: A353490 A377051 A226131 * A334318 A199056 A377038

Adjacent sequences: A375034 A375035 A375036 * A375038 A375039 A375040

KEYWORD

nonn,tabf,easy

AUTHOR

Omar E. Pol, Jul 28 2024

STATUS

approved