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A262432 Regular triangle read by rows: T(n, k) gives the number of times that the denominator of sigma(x,-1) (A017666) is equal to k when x goes from 1 to n. 2
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 0, 2, 1, 1, 1, 1, 0, 1, 2, 1, 1, 1, 1, 0, 1, 1, 2, 1, 1, 1, 1, 0, 1, 1, 1, 2, 1, 1, 1, 2, 0, 1, 1, 1, 0, 2, 1, 1, 1, 2, 0, 1, 1, 1, 0, 1, 2, 1, 2, 1, 2, 0, 1, 1, 1, 0, 1, 0, 2, 1, 2, 1, 2, 0, 1, 1, 1, 0, 1, 0, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,16

COMMENTS

The sum of terms of the n-th row is n.

T(n, n) = 1 when n is in A014567.

T(n, n) = 0 when n is in A069059.

T(n, 1) increases when n is a multiperfect number A007691.

For a given k, the first index n for which T(n,k) = 1 is A162657(k).

LINKS

Michel Marcus, Table of n, a(n) for n = 1..5050

EXAMPLE

The first 6 terms of A017666 are 1, 2, 3, 4, 5, 1 where 1 appears twice, 2 to 5 appear once and 6 is absent; giving the 6th row: 2, 1, 1, 1, 1, 0.

Triangle starts

1;

1, 1;

1, 1, 1;

1, 1, 1, 1;

1, 1, 1, 1, 1;

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

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

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

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

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

...

MATHEMATICA

Table[Length@ Select[Range@ n, Denominator[DivisorSigma[-1, #]] == k &], {n, 13}, {k, n}] // Flatten (* Michael De Vlieger, Sep 22 2015 *)

PROG

(PARI) tabl(nn) = {vds = vector(nn, n, denominator(sigma(n, -1))); for (n=1, nn, vin = vector(n, k, vds[k]); rown = vector(n, k, #select(x->x==k, vin)); for(k=1, n, print1(rown[k], ", ")); print(); ); }

CROSSREFS

Cf. A007691, A014567, A017666, A069059, A162657.

Sequence in context: A080234 A136049 A225192 * A135694 A025924 A025904

Adjacent sequences:  A262429 A262430 A262431 * A262433 A262434 A262435

KEYWORD

nonn,tabl

AUTHOR

Michel Marcus, Sep 22 2015

STATUS

approved

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Last modified August 26 03:21 EDT 2019. Contains 326324 sequences. (Running on oeis4.)