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

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

Offset

1,1

Comments

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

Links

Felix Fröhlich, Table of n, a(n) for n = 1..10000

G. L. Honaker, Jr. and Chris Caldwell, Prime Curios!, Number 1729.

Example

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

Mathematica

Module[{nn=40, prs}, prs=Select[6*Range[nn]+1, PrimeQ]; Take[Times@@@ Subsets[ prs, {3}]//Union, nn]] (* Harvey P. Dale, Feb 17 2018 *)

Prog

(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

Crossrefs

Subsequence of A007304.

Cf. A001235, A002476, A011541, A154716, A154717, A154728.

Sequence in context: A033181 A300949 A198775 * A083737 A182208 A340092

Adjacent sequences: A154726 A154727 A154728 * A154730 A154731 A154732

Keyword

nonn

Author

Omar E. Pol, Jan 18 2009

Extensions

a(5)-a(38) from Donovan Johnson, Jan 28 2009

Status

approved