A318498 -id:A318498 - cp's OEIS frontend

A318499 The 2-adic valuation of A318498.

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

Offset: 1

Antti Karttunen, Aug 30 2018

nonn

Antti Karttunen, Table of n, a(n) for n = 1..65537

Cf. A318498.

A318499(n) = valuation(A318498(n),2); \\ Needs also code from A318498.

a(n) = A007814(A318498(n)).

A318672 Denominators of the sequence whose Dirichlet convolution with itself yields A049599, number of (1+e)-divisors of n.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1

Offset: 1

Antti Karttunen, Sep 03 2018

The sequence seems to give the denominators of a few other similarly constructed rational valued sequences obtained as "Dirichlet Square Roots" (possibly of A282446 and A318469).

Antti Karttunen, Table of n, a(n) for n = 1..16385

Cf. A049599, A318671 (numerators), A318673.

Cf. also A046644, A299150, A317932, A317934, A318498.

up_to = (2^16)+1;
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&&dA049599(n) = factorback(apply(e -> (1+numdiv(e)),factor(n)[,2]));
v318671_62 = DirSqrt(vector(up_to, n, A049599(n)));
A318671(n) = numerator(v318671_62[n]);
A318672(n) = denominator(v318671_62[n]);
A318673(n) = valuation(A318672(n),2);

a(n) = denominator of f(n), where f(1) = 1, f(n) = (1/2) * (A049599(n) - Sum_{d|n, d>1, d 1.

a(n) = 2^A318673(n).

A318497 Numerators of the sequence whose Dirichlet convolution with itself yields A061389, number of (1+phi)-divisors of n.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 13, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -13, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 13, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset: 1

Antti Karttunen, Aug 30 2018

No zeros among the first 2^20 terms. This is most probably multiplicative, like A318498.

Antti Karttunen, Table of n, a(n) for n = 1..65537

Cf. A061389, A318314 (denominators).

up_to = 65537;
A061389(n) = factorback(apply(e -> (1+eulerphi(e)),factor(n)[,2]));
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&&dA317937.
v318497_98 = DirSqrt(vector(up_to, n, A061389(n)));
A318497(n) = numerator(v318497_98[n]);

a(n) = numerator of f(n), where f(1) = 1, f(n) = (1/2) * (A061389(n) - Sum_{d|n, d>1, d 1.

cp's OEIS Frontend

A318499 The 2-adic valuation of A318498.

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A318672 Denominators of the sequence whose Dirichlet convolution with itself yields A049599, number of (1+e)-divisors of n.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

PARI

Formula

A318497 Numerators of the sequence whose Dirichlet convolution with itself yields A061389, number of (1+phi)-divisors of n.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

PARI

Formula