cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A154729 Products of three distinct primes of the form 6*k + 1.

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%I A154729 #26 Jul 20 2021 11:34:38
%S A154729 1729,2821,3367,3913,4123,4921,5551,5719,6097,6643,7189,7657,8029,
%T A154729 8113,8827,8911,9139,9331,9373,9709,9919,10507,10621,11137,11557,
%U A154729 12649,12901,13237,13699,13741,14287,14497,14539,14833,14911,15067,15799,15841
%N A154729 Products of three distinct primes of the form 6*k + 1.
%C A154729 a(1) = 1729 is the Hardy-Ramanujan number (see taxicab numbers in A001235, A011541).
%C A154729 Equivalently, products of three distinct primes of the form 3*k + 1. - _Omar E. Pol_, Feb 17 2018
%H A154729 Felix Fröhlich, <a href="/A154729/b154729.txt">Table of n, a(n) for n = 1..10000</a>
%H A154729 G. L. Honaker, Jr. and Chris Caldwell, <a href="https://primes.utm.edu/curios/page.php?number_id=94&amp;submitter=Pol">Prime Curios!</a>, Number 1729.
%e A154729 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
%t A154729 Module[{nn=40,prs},prs=Select[6*Range[nn]+1,PrimeQ];Take[Times@@@ Subsets[ prs,{3}]//Union,nn]] (* _Harvey P. Dale_, Feb 17 2018 *)
%o A154729 (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
%o A154729 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
%Y A154729 Subsequence of A007304.
%Y A154729 Cf. A001235, A002476, A011541, A154716, A154717, A154728.
%K A154729 nonn
%O A154729 1,1
%A A154729 _Omar E. Pol_, Jan 18 2009
%E A154729 a(5)-a(38) from _Donovan Johnson_, Jan 28 2009