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%I #28 Feb 19 2019 11:10:51
%S 4,8,9,16,21,25,27,32,36,45,49,64,81,87,91,99,121,125,128,144,169,196,
%T 217,243,256,289,325,343,361,400,417,481,512,529,559,625,685,697,703,
%U 721,729,745,749,775,801,841,925,931,961,1024,1156,1157,1261,1331
%N Composite numbers n such that sum of proper divisors of n divides sum of proper divisors of n^n.
%C Terms are 2^2, 2^3, 3^2, 2^4, 3*7, 5^2, 3^3, 2^5, 2^2*3^2, 3^2*5, 7^2, 2^6, 3^4, 3*29, 7*13, 3^2*11, 11^2, 5^3, ...
%C Terms that are not Duffinian numbers are 45, 87, 91, 99, 196, 703, 745, 775, 801, 931, ...
%e Composite number 21 is a term because (sigma(21) - 21) = 11 divides (sigma(21^21) - 21^21) = 4381940263463668467705506011
%t Select[Range[10^3], And[CompositeQ@ #, Divisible @@ Map[DivisorSigma[1, #] - # &, {#^#, #}]] &] (* _Michael De Vlieger_, Jan 02 2017 *)
%o (PARI) is(n) = !isprime(n) && (sigma(n^n)-n^n)%(sigma(n)-n)==0;
%Y Cf. A000203, A001065, A003624, A275123.
%K nonn,less
%O 1,1
%A _Altug Alkan_, Jan 01 2017
%E More terms from _Amiram Eldar_, Feb 19 2019
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