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

1,1

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

Links

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

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

Example

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.

Crossrefs

Cf. A001235, A154729, A193869, A193873.

Sequence in context: A337316 A338998 A280428 * A339818 A293649 A272885

Adjacent sequences: A194260 A194261 A194262 * A194264 A194265 A194266

Keyword

nonn

Author

Omar E. Pol, Sep 02 2011

Status

approved