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%I #12 Jul 21 2021 00:44:24
%S 1,2,4,8,16,32,64,105,225,315,1155,2475,4455,8775,26325,27027,63063,
%T 106029,247401,693693,829521,969969,2241603,3741309,7894341,8083075,
%U 32569173,33671781,37182145,56581525,146791359,185910725,622396775,929553625,1301375075
%N Highly composite deficient numbers: deficient numbers k whose number of divisors d(k) > d(m) for all deficient numbers m < k.
%C The record numbers of divisors are 1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 16, 18, 20, 24, 30, 32, 36, 40, 48, 54, 60, 64, 72, 80, 84, 96, 108, 112, 128, 144, 160, 192, 216, 256, 288, ...
%t a={}; dm=0; Do[ If[DivisorSigma[1,n]>=2n, Continue[]]; d=DivisorSigma[0,n]; If[d>dm, dm=d; AppendTo[a,n]], {n,1,1000000}]; a
%o (PARI) lista(nn) = {my(maxd = 0); for (n=1, nn, if ((sigma(n) < 2*n) && (numdiv(n) > maxd), maxd = numdiv(n); print1(n, ", ");););} \\ _Michel Marcus_, Apr 17 2018
%Y Cf. A000005, A002182, A005100.
%K nonn
%O 1,2
%A _Amiram Eldar_, Apr 16 2018
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