A194263 Numbers that occur more than once in A193873, in order of appearance.

1729, 13981, 88537, 51319, 137149, 548497, 285541, 3372529, 18326641, 1152271, 1809641, 3828001, 4814857, 4797703, 79230049, 4413223, 4209661, 19703611, 3882139, 50357677, 70611161, 26536591, 175493677, 85409941, 12932989, 84350561, 192754871, 59756863

Offset: 1

Author

Omar E. Pol, Sep 02 2011

Keywords

• nonn

Comments

Note that a(1) = 1729 is known as the Hardy-Ramanujan number (see A001235).

Apparently these numbers occur only twice in A193873.

Many of these numbers occur more than twice. For example, 812405017 occurs 3 times, a(67), a(134), and a(268). Robert Price, Mar 17 2020

Examples

			1729 is in the sequence because the Hardy-Ramanujan number is also the smallest product of three distinct primes of the form 3*k+1 and also of the form 6*k+1, so 1729 occurs more than once in A193873.
		

Links

• Robert Price, Table of n, a(n) for n = 1..2554

Crossrefs

Cf. A001235, A154729, A193869, A193873.

Formula

It appears that a(n) = A193873(2*n+1).

This conjecture only holds for n<62: a(62)=A193873(124)=A193873(2n)=620378449

, a(63)=A193873(125)=A193873(2n-1)=424315751

. Robert Price, Mar 17 2020