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A154729
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Products of three distinct primes of the form 6*k + 1.
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7
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1729, 2821, 3367, 3913, 4123, 4921, 5551, 5719, 6097, 6643, 7189, 7657, 8029, 8113, 8827, 8911, 9139, 9331, 9373, 9709, 9919, 10507, 10621, 11137, 11557, 12649, 12901, 13237, 13699, 13741, 14287, 14497, 14539, 14833, 14911, 15067, 15799, 15841
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OFFSET
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1,1
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COMMENTS
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a(1) = 1729 is the Hardy-Ramanujan number (see taxicab numbers in A001235, A011541).
Equivalently, products of three distinct primes of the form 3*k + 1. - Omar E. Pol, Feb 17 2018
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LINKS
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G. L. Honaker, Jr. and Chris Caldwell, Prime Curios!, Number 1729.
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EXAMPLE
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The first three primes of the form 6*k + 1 are 7, 13 and 19, so a(1) = 7*13*19 = 1729. - Omar E. Pol, Feb 17 2018
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MATHEMATICA
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Module[{nn=40, prs}, prs=Select[6*Range[nn]+1, PrimeQ]; Take[Times@@@ Subsets[ prs, {3}]//Union, nn]] (* Harvey P. Dale, Feb 17 2018 *)
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PROG
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(PARI) fct(n, o=[1])=if(n>1, concat(apply(t->vector(t[2], i, t[1]), Vec(factor(n)~))), o) \\ after M. F. Hasler in A027746
is(n) = my(f=fct(n)); if(#f!=3 || f!=vecsort(f, , 8), return(0), for(k=1, #f, if((f[k]-1)/6!=ceil((f[k]-1)/6), return(0)))); 1 \\ Felix Fröhlich, Jul 07 2021
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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