A378633 Numbers having a self-conjugate multiplicative partition into primes.

1, 4, 18, 27, 200, 300, 1125, 1568, 2352, 3125, 8820, 24500, 27783, 61952, 77175, 92928, 346112, 348480, 420175, 519168, 823543, 968000, 1097712, 1946880, 3049200, 5408000, 6132672, 8732691, 9469952, 14204928, 16601200, 17035200, 24257475, 32538352, 47316992

Offset

1,2

Links

Table of n, a(n) for n=1..35.

Eric Weisstein's World of Mathematics, Self Conjugate Partition

Wikipedia, Integer partition (Conjugate and self-conjugate partitions

Example

200 is in the sequence because the prime decomposition 5*5*2*2*2 can be represented by this multiplicative partition that has mirror symmetry about the x=y axis:
   XX
   XX
   XX
   XXXXX
   XXXXX
300 is in the sequence because the prime decomposition 5*5*3*2*2 can be represented by this multiplicative partition that has mirror symmetry about the x=y axis:
   XX
   XX
   XXX
   XXXXX
   XXXXX

Crossrefs

Cf. A051674 (subsequence).

Sequence in context: A358375 A166749 A370406 * A103067 A080519 A120407

Adjacent sequences: A378630 A378631 A378632 * A378634 A378636 A378637

Keyword

nonn,new

Author

Gordon Hamilton, Dec 02 2024

Extensions

More terms from Alois P. Heinz, Dec 02 2024

Status

approved