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%I #8 Mar 13 2019 23:49:35
%S 1,4,8,16,36,72,108,144,216,288,1800,3600,7200
%N Highly abundant numbers that are powerful.
%C Alaoglu and Erdős proved that 7200 is the last term.
%C Intersection of A001694 and A002093.
%H Leonidas Alaoglu and Paul Erdős, <a href="https://doi.org/10.1090/S0002-9947-1944-0011087-2">On highly composite and similar numbers</a>, Transactions of the American Mathematical Society, Vol. 56, No. 3 (1944), pp. 448-469.
%t seq={1}; sm = 0; Do[s = DivisorSigma[1, n]; If[s>sm, sm = s; If[ Min @ FactorInteger[n][[;;, 2]] > 1, AppendTo[seq, n]]], {n, 2, 72000}]; seq
%Y Cf. A001694, A002093.
%K nonn,fini,full
%O 1,2
%A _Amiram Eldar_, Mar 01 2019
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