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%I #23 Aug 21 2024 11:38:48
%S 1,20,64,500,729,1024,1280,4096,4352,14580,15625,32000,39168,46656,
%T 47360,59049,65536,117649,144640,161024,262144,312500,364500,509184,
%U 531441,746496,796797,933120,1000000,1180980,1184000,1449216,1771561
%N Numbers k such that the sum of 2nd, 3rd, 4th and 5th powers of divisors of k are divisible by sum of divisors of k.
%H Amiram Eldar, <a href="/A074632/b074632.txt">Table of n, a(n) for n = 1..269</a> (terms up to 10^10)
%e For k = 20: sigma(k) = 42 ,sigma_2(k) = 546 = 13 * 42, sigma_3(k) = 9198 = 219 * 42, sigma_4(k) = 170898 = 4069 * 42, sigma_5(k) = 3304182 = 78671 * 42.
%t Select[Range[2000000],And@@Divisible[DivisorSigma[Range[2,5],#], DivisorSigma[ 1,#]]&] (* _Harvey P. Dale_, Jan 01 2012 *)
%o (PARI) is(k) = {my(f = factor(k), s = sigma(f)); for(k = 2, 5, if(sigma(f, k) % s, return(0))); 1; } \\ _Amiram Eldar_, Jun 15 2024
%Y See also A020487, A046841, A046870, A046871.
%Y Cf. A000203, A001157, A001158, A001159, A001160.
%K nonn
%O 1,2
%A _Labos Elemer_, Aug 27 2002
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