A134676 - OEIS

A134676

Triangle read by rows: A127172 * A127648 as infinite lower triangular matrices.

1, 3, 2, 3, 0, 3, 6, 6, 0, 4, 3, 0, 0, 0, 5, 9, 6, 9, 0, 0, 6, 3, 0, 0, 0, 0, 0, 7, 10, 12, 0, 12, 0, 0, 0, 8, 6, 0, 9, 0, 0, 0, 0, 0, 9, 9, 6, 0, 0, 15, 0, 0, 0, 0, 10, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11, 18, 18, 18, 12, 0, 18, 0, 0, 0, 0, 0, 12, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13

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OFFSET

1,2

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..1275 (first 50 rows)

FORMULA

Equals A127172 * A127648 = A051731^3 * A127648 as infinite lower triangular matrices.

T(n,k) = k*A127172(n,k). - Andrew Howroyd, Sep 23 2025

EXAMPLE

First few rows of the triangle:

3, 2;

3, 0, 3;

6, 6, 0, 4;

3, 0, 0, 0, 5;

9, 6, 9, 0, 0, 6;

3, 0, 0, 0, 0, 0, 7;

...

MATHEMATICA

A134676[n_, k_] := If[Divisible[n, k], k*DivisorSum[n/k, DivisorSigma[0, #] &], 0];

Table[A134676[n, k], {n, 15}, {k, n}] (* Paolo Xausa, Sep 23 2025 *)

PROG

(PARI) T(n, k) = if(n%k, 0, k*sumdiv(n/k, d, numdiv(d))) \\ Andrew Howroyd, Sep 23 2025

CROSSREFS

Column 1 is A007425.

Row sums are A007430.

Cf. A051731, A127093, A127648, A127172, A134577.

Sequence in context: A230409 A244543 A283979 * A286246 A286249 A239146

Adjacent sequences: A134673 A134674 A134675 * A134677 A134678 A134679

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson, Nov 05 2007

EXTENSIONS

a(56) onwards from Andrew Howroyd, Sep 23 2025

STATUS

approved