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 A357700 Noncubefree numbers k such that A073185(k) > 2*k. 1

%I #9 Oct 12 2022 04:13:46

%S 360360,471240,1801800,2356200,2522520,2633400,2784600,3112200,

%T 3187800,3298680,3686760,3767400,3898440,3963960,4019400,4296600,

%U 4462920,4684680,5128200,5183640,5682600,5793480,6126120,6846840,8011080,8288280,8953560,10210200,10450440

%N Noncubefree numbers k such that A073185(k) > 2*k.

%C The cubefree numbers k such that A073185(k) > 2*k are the cubefree abundant numbers (A357695).

%C The least odd term is (3/4) * prime(13)# * prime(197)# = 6.252...*10^517.

%H Amiram Eldar, <a href="/A357700/b357700.txt">Table of n, a(n) for n = 1..10000</a>

%e 360360 = 2^3 * 45045 is a term since it is divisible by a cube and A073185(360360) = 733824 > 2*360360.

%t f[p_, e_] := 1 + p + If[e == 1, 0, p^2]; q[n_] := AnyTrue[(fct = FactorInteger[n])[[;;, 2]], # > 2 &] && Times @@ f @@@ fct > 2*n; Select[Range[2, 5*10^6], q]

%o (PARI) is(n) = {my(f = factor(n)); if(n == 1 || vecmax(f[,2]) < 3, return(0)); prod(i=1, #f~, 1 + f[i,1] + if(f[i,2]==1, 0, f[i,1]^2)) > 2*n};

%Y Cf. A073185, A357695.

%K nonn

%O 1,1

%A _Amiram Eldar_, Oct 10 2022

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Last modified August 13 13:57 EDT 2024. Contains 375142 sequences. (Running on oeis4.)