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A317848 Multiplicative with a(p^e) = binomial(2*e, e). 3
1, 2, 2, 6, 2, 4, 2, 20, 6, 4, 2, 12, 2, 4, 4, 70, 2, 12, 2, 12, 4, 4, 2, 40, 6, 4, 20, 12, 2, 8, 2, 252, 4, 4, 4, 36, 2, 4, 4, 40, 2, 8, 2, 12, 12, 4, 2, 140, 6, 12, 4, 12, 2, 40, 4, 40, 4, 4, 2, 24, 2, 4, 12, 924, 4, 8, 2, 12, 4, 8, 2, 120, 2, 4, 12, 12, 4, 8, 2, 140 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The Dirichlet convolution square of this sequence is A165825.

LINKS

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

FORMULA

A037445(n) = A006519(a(n)).

A046643(n) = numerator(a(n)/A165825(n)) = A000265(a(n)).

A046644(n) = denominator(a(n)/A165825(n)) = A165825(n)/A037445(n).

A299149(n) = numerator(n*a(n)/A165825(n)) = A000265(n*a(n)).

A299150(n) = denominator(n*a(n)/A165825(n)) = A165825(n)/(A037445(n) * A006519(n)).

PROG

(PARI) a(n)={my(v=factor(n)[, 2]); prod(i=1, #v, binomial(2*v[i], v[i]))}

(PARI) \\ DirSqrt(v) finds u such that v = v[1]*dirmul(u, u).

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}

DirSqrt(vector(80, n, 4^bigomega(n)))

(PARI) A317848(n) = factorback(apply(e -> binomial(e+e, e), factor(n)[, 2])); \\ Antti Karttunen, Sep 17 2018

CROSSREFS

Cf. A000265, A000984, A006519, A037445, A046643, A046644, A165825, A299149, A299150.

Sequence in context: A265392 A253139 A318519 * A124859 A021446 A062401

Adjacent sequences:  A317845 A317846 A317847 * A317849 A317850 A317851

KEYWORD

nonn,mult

AUTHOR

Andrew Howroyd, Aug 08 2018

STATUS

approved

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Last modified May 21 08:51 EDT 2019. Contains 323441 sequences. (Running on oeis4.)