A378633 - OEIS

%I #28 Mar 31 2025 01:47:50

%S 1,4,18,27,200,300,1125,1568,2352,3125,8820,24500,27783,61952,77175,

%T 92928,346112,348480,420175,519168,823543,968000,1097712,1946880,

%U 3049200,5408000,6132672,8732691,9469952,14204928,16601200,17035200,24257475,32538352,47316992

%N Numbers having a self-conjugate multiplicative partition into primes.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Self-ConjugatePartition.html">Self Conjugate Partition</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Integer_partition#Conjugate_and_self-conjugate_partitions">Integer partition (Conjugate and self-conjugate partitions)</a>

%e 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:

%e    XX

%e    XX

%e    XX

%e    XXXXX

%e    XXXXX

%e 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:

%e    XX

%e    XX

%e    XXX

%e    XXXXX

%e    XXXXX

%Y Cf. A051674 (subsequence).

%K nonn

%O 1,2

%A _Gordon Hamilton_, Dec 02 2024

%E More terms from _Alois P. Heinz_, Dec 02 2024