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A131907
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Integers for which a smaller positive integer exists which has the same sum of cubes of its divisors.
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3
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194315, 295301, 2953010, 1181204, 1476505, 1886920, 2067107, 2362408, 2526095, 2953010, 3248311, 3691985, 3838913, 4134214, 4469245, 4724816, 5020117, 5610719, 5635135, 5906020, 6023765, 6496622, 6791923, 7382525, 7677826
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OFFSET
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1,1
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LINKS
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FORMULA
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n-th element of {x>0: there exists a k with 0<k<x and the same sum of the cubes of its divisors as x)
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EXAMPLE
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a(1)=194315 because it is the least integer for which a smaller positive integer with the same sum of the cubes of its divisors exist. The sum of the cubes of 194315 is 1+125+1331+166375+44099220437+5512402554625+58696062401647+7337007800205875=7401260364550416.
The sum of the cubes of 184926 is 1 + 8 + 27 + 216 + 343 + 2744 + 4913 + 9261 + 39304 + 50653 + 74088 + 117649 + 132651 + 405224 + 941192 + 1061208 + 1367631 + 1685159 + 3176523 + 10941048 + 13481272 + 17373979 + 25412184 + 45499293 + 138991832 + 248858189 + 363994344 + 469097433 + 578009537 + 1990865512 + 3752779464 + 4624076296 + 5959274797 + 6719171103 + 15606257499 + 47674198376 + 53753368824 + 85358358827 + 124850059992 + 160900419519 + 682866870616 + 1287203356152 + 2304675688329 + 18437405506632 + 29277917077661 + 234223336621288 + 790503761096847 + 6324030088774776=7401260364550416, which is the same.
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MATHEMATICA
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First@Transpose[Reap[For[n = 1, n <= 5*10^6, n++, (If[Head[ #1] === tmp, #1 = n, Sow[{n, #1}]] & )[ tmp[DivisorSigma[3, n]]]]][[2, 1]]]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Peter Pein (petsie(AT)dordos.net), Jul 26 2007, Jul 28 2007
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EXTENSIONS
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More terms from Max Alekseyev and Daniel Lichtblau (danl(AT)wolfram.com), Jul 28 2007
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STATUS
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approved
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