A294721 - OEIS

A294721

Irregular triangle read by rows: T(n,k) = n if k is the largest divisor of n <= sqrt(n), otherwise T(n,k) = 0. The first element of column k is in row k^2, n>=1, k>=1.

1, 2, 3, 0, 4, 5, 0, 0, 6, 7, 0, 0, 8, 0, 0, 9, 0, 10, 0, 11, 0, 0, 0, 0, 12, 13, 0, 0, 0, 14, 0, 0, 0, 15, 0, 0, 0, 16, 17, 0, 0, 0, 0, 0, 18, 0, 19, 0, 0, 0, 0, 0, 0, 20, 0, 0, 21, 0, 0, 22, 0, 0, 23, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 25, 0, 26, 0, 0, 0, 0, 0, 27, 0, 0, 0, 0, 0, 28, 0, 29, 0, 0, 0, 0, 0, 0, 0, 0, 30

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OFFSET

1,2

LINKS

Table of n, a(n) for n=1..100.

Omar E. Pol,Illustration of initial terms

FORMULA

T(n,A033676(n)) = n.

T(n,k) = 0, if k is not equal toA033676(n), n >= 1, and 1 <= k <=A000196(n).

T(n,k) = n*A294821(n,k).

EXAMPLE

Triangle begins:

0, 4;

5, 0;

0, 6;

7, 0;

0, 8;

0, 0, 9;

0, 10, 0;

11, 0, 0;

0, 0, 12;

13, 0, 0;

0, 14, 0;

0, 0, 15;

0, 0, 0, 16;

17, 0, 0, 0;

0, 0, 18, 0;

19, 0, 0, 0;

0, 0, 0, 20;

0, 0, 21, 0;

0, 22, 0, 0;

23, 0, 0, 0;

0, 0, 0, 24;

0, 0, 0, 0, 25;

...

CROSSREFS

Cf.A033676,A163280,A294821.

Row n has lengthA000196(n).

Row sums giveA000027.

Positive terms also giveA000027.

Positive terms of column k, for k = 1..12, give respectively:A008578,A161344,A161345,A161424,A161835,A162526,A162527,A162528,A162529,A162530,A162531,A162532.

Sequence in context:A154860 A284282 A132774*A300816 A007945 A011150

Adjacent sequences:A294718 A294719 A294720*A294722 A294723 A294724

KEYWORD

nonn,tabf

AUTHOR

Omar E. Pol,Nov 07 2017

STATUS

approved