A318681 a(n) = n * A299149(n).

1, 2, 9, 12, 25, 18, 49, 40, 243, 50, 121, 108, 169, 98, 225, 560, 289, 486, 361, 300, 441, 242, 529, 360, 1875, 338, 3645, 588, 841, 450, 961, 2016, 1089, 578, 1225, 2916, 1369, 722, 1521, 1000, 1681, 882, 1849, 1452, 6075, 1058, 2209, 5040, 7203, 3750, 2601, 2028, 2809, 7290, 3025, 1960, 3249, 1682, 3481, 2700

Offset

1,2

Comments

Dirichlet convolution of a(n)/A299150(n) with itself gives A000290, the squares, like gives also the self-convolution of A318649(n)/A318512(n), as it is the same ratio reduced to its lowest terms. However, in contrast to A318649, this sequence is multiplicative as both A000027 and A299149 are multiplicative sequences (also, because A000290 and A299150 are both multiplicative).

A007814 gives the 2-adic valuation of this sequence, because there are no even terms in A299149.

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Wikipedia, Dirichlet convolution

Formula

a(n) = n * A299149(n).

a(n)/A299150(n) = A318649(n)/A318512(n).

Prog

(PARI)
up_to = 65537;
DirSqrt(v) = {my(n=#v, u=vector(n)); u[1]=1; for(n=2, n, u[n]=(v[n]/v[1] -
sumdiv(n, d, if(d>1&&d<n, u[d]*u[n/d], 0)))/2); u};
v299149_50 = DirSqrt(vector(up_to, n, n));
A299149(n) = numerator(v299149_50[n]);
A318681(n) = (n*A299149(n));

Crossrefs

Cf. A000290, A299149, A299150, A318512, A318649, A318680.

Sequence in context: A273669 A129829 A053900 * A183207 A347496 A304797

Adjacent sequences: A318678 A318679 A318680 * A318682 A318683 A318684

Keyword

nonn,mult

Author

Antti Karttunen, Sep 02 2018

Status

approved