A358865 - OEIS

%I #9 Dec 06 2022 09:52:17

%S 20,140,405,2856,25296,111720,25984,5474000,237600,223826688,3852800,

%T 268565760,1834725376,175861400000,335674368,2863363937280,

%U 4383831556096,206015846400,3400704000,938209120583680,2981338216980480,21463949229465600,45410367307776,72056803765911552

%N a(n) is the smallest n-gonal pyramidal number with exactly n prime factors (counted with multiplicity).

%C The corresponding indices of n-gonal pyramidal numbers are 4, 7, 9, 16, 31, 48, 28, 160, 54, 512, 128, 512, 946, 4224, 512, 10240, 11566, 4095, 1024, ...

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimeFactor.html">Prime Factor</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PyramidalNumber.html">Pyramidal Number</a>

%e a(3) = 20, because 20 is a tetrahedral (or triangular pyramidal) number with 3 prime factors (counted with multiplicity) {2, 2, 5} and this is the smallest such number.

%o (PARI) a(n) = if(n<3, return()); for(k=1, oo, my(t=(k*(k+1)*((n-2)*k + (5-n)))\6); if(bigomega(t) == n, return(t))); \\ _Daniel Suteu_, Dec 05 2022

%Y Cf. A001222, A358862, A358863, A358864.

%K nonn

%O 3,1

%A _Ilya Gutkovskiy_, Dec 03 2022

%E a(22)-a(26) from _Daniel Suteu_, Dec 05 2022