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A127170 Triangle, square of A051731. 9
1, 2, 1, 2, 0, 1, 3, 2, 0, 1, 2, 0, 0, 0, 1, 4, 2, 2, 0, 0, 1, 2, 0, 0, 0, 0, 0, 1, 4, 3, 0, 2, 0, 0, 0, 1, 3, 0, 2, 0, 0, 0, 0, 0, 1, 4, 2, 0, 0, 2, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 6, 4, 3, 2, 0, 2, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 4, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Nonzero terms in every column = d(n), A000005: (1, 2, 2, 3, 2, 4, 2, 4,...). Row sums = A007425: (1, 3, 3, 6, 3, 9, 3, 10,...). A127170 * [1, 0, 0, 0,...] = A000005: (1, 2, 2, 3, 2, 4,...) A127170 * [1, 2, 3,...] = A007429: (1, 4, 10, 4, 16,...).

Eigensequence of the triangle = A007557; i.e., sequence A007557 shifts to the left upon multiplication by A127170. - Gary W. Adamson, Apr 27 2009

T(n,k) is also the number of divisors of n that are divisible by k, with n>=1 and 1<=k<=n (see also A195050). - Omar E. Pol, Mar 30 2015

LINKS

Table of n, a(n) for n=1..105.

FORMULA

Square of A051731 A000005, d(n); in every column k, interspersed with (k-1) zeros.

T(n,k) = A000005(n/k), if k divides n, otherwise 0, with n>=1 and 1<=k<=n. - Omar E. Pol, Apr 01 2015

EXAMPLE

First 10 rows of the triangle are:

1;

2, 1;

2, 0, 1;

3, 2, 0, 1;

2, 0, 0, 0, 1;

4, 2, 2, 0, 0, 1;

2, 0, 0, 0, 0, 0, 1;

4, 3, 0, 2, 0, 0, 0, 1;

3, 0, 2, 0, 0, 0, 0, 0, 1;

4, 2, 0, 0, 2, 0, 0, 0, 0, 1;

...

PROG

(PARI) tabl(nn) = {m = matrix(nn, nn, n, k, if ((n % k) == 0, 1, 0)); m = m^2; for (n=1, nn, for (k=1, n, print1(m[n, k], ", "); ); print(); ); } \\ Michel Marcus, Apr 01 2015

CROSSREFS

Cf. A051731, A000005, A007425, A126988, A007429, A127170.

Cf. A007557. - Gary W. Adamson, Apr 27 2009

Sequence in context: A028933 A190491 A143352 * A143335 A099505 A156837

Adjacent sequences:  A127167 A127168 A127169 * A127171 A127172 A127173

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson, Jan 06 2007

EXTENSIONS

8 terms taken from Example section and then corrected in Data section by Omar E. Pol, Mar 30 2015

Extended beyond a(21) by Omar E. Pol, Apr 01 2015

STATUS

approved

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Last modified September 20 12:31 EDT 2017. Contains 292271 sequences.