login
A358865
a(n) is the smallest n-gonal pyramidal number with exactly n prime factors (counted with multiplicity).
7
20, 140, 405, 2856, 25296, 111720, 25984, 5474000, 237600, 223826688, 3852800, 268565760, 1834725376, 175861400000, 335674368, 2863363937280, 4383831556096, 206015846400, 3400704000, 938209120583680, 2981338216980480, 21463949229465600, 45410367307776, 72056803765911552
OFFSET
3,1
COMMENTS
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, ...
LINKS
Eric Weisstein's World of Mathematics, Prime Factor
Eric Weisstein's World of Mathematics, Pyramidal Number
EXAMPLE
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.
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Dec 03 2022
EXTENSIONS
a(22)-a(26) from Daniel Suteu, Dec 05 2022
STATUS
approved