The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A034676 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A034676

Sum of squares of unitary divisors of n.
(history; published version)

#32 by R. J. Mathar at Fri Jul 12 10:12:05 EDT 2024

STATUS

editing

approved

#31 by R. J. Mathar at Fri Jul 12 10:12:01 EDT 2024

MAPLE

A034676 := proc(n)

a :=1 ;

for pe in ifactors(n)[2] do

p := op(1, pe) ;

e := op(2, pe) ;

a := a*(p^(2*e)+1) ;

end do:

a ;

end proc:

seq(A034676(n), n=1..40) ; # R. J. Mathar, Jul 12 2024

STATUS

approved

editing

#30 by Vaclav Kotesovec at Sun Sep 20 09:11:37 EDT 2020

STATUS

editing

approved

#29 by Vaclav Kotesovec at Sun Sep 20 09:11:29 EDT 2020

FORMULA

Sum_{k>=1} 1/a(k) = 1.5594563610641446770272272038182777336348840179730233519185104374159616326... - Vaclav Kotesovec, Sep 20 2020

STATUS

approved

editing

#28 by Bruno Berselli at Mon Sep 14 02:55:48 EDT 2020

STATUS

proposed

approved

#27 by Amiram Eldar at Mon Sep 14 01:49:26 EDT 2020

STATUS

editing

proposed

#26 by Amiram Eldar at Mon Sep 14 01:33:33 EDT 2020

LINKS

Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/UnitaryDivisorFunction.html">Unitary Divisor Function</a>.

Wikipedia, <a href="http://en.wikipedia.org/wiki/Unitary_divisor">Unitary divisor</a>.

#25 by Amiram Eldar at Mon Sep 14 01:33:09 EDT 2020

MATHEMATICA

f[p_, e_] := p^(2*e)+1; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Sep 14 2020 *)

STATUS

approved

editing

#24 by Vaclav Kotesovec at Fri Jan 11 12:59:20 EST 2019

STATUS

editing

approved

#23 by Vaclav Kotesovec at Fri Jan 11 12:59:15 EST 2019

FORMULA

Sum_{k=1..n} a(k) ~ 30 * Zeta(3) * n^3 / Pi^4. - Vaclav Kotesovec, Jan 11 2019

STATUS

approved

editing