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A074632
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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.
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1
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1, 20, 64, 500, 729, 1024, 1280, 4096, 4352, 14580, 15625, 32000, 39168, 46656, 47360, 59049, 65536, 117649, 144640, 161024, 262144, 312500, 364500, 509184, 531441, 746496, 796797, 933120, 1000000, 1180980, 1184000, 1449216, 1771561
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OFFSET
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1,2
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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Select[Range[2000000], And@@Divisible[DivisorSigma[Range[2, 5], #], DivisorSigma[ 1, #]]&] (* Harvey P. Dale, Jan 01 2012 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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