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A358864
a(n) is the smallest n-gonal pyramidal number with exactly n distinct prime factors.
6
84, 1785, 299880, 1020510, 8897460, 102612510, 33367223274, 249417828660, 9177835927260, 10064864238489060, 5558913993302670, 15633689593760207970, 3792821921183752657200
OFFSET
3,1
COMMENTS
The corresponding indices of n-gonal pyramidal numbers are 7, 17, 84, 115, 220, 468, 3058, 5719, 18290, ...
LINKS
Eric Weisstein's World of Mathematics, Distinct Prime Factors
Eric Weisstein's World of Mathematics, Pyramidal Number
EXAMPLE
a(3) = 84, because 84 is a tetrahedral (or triangular pyramidal) number with 3 distinct prime factors {2, 3, 7} 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(omega(t) == n, return(t))); \\ Daniel Suteu, Dec 05 2022
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Ilya Gutkovskiy, Dec 03 2022
EXTENSIONS
a(12)-a(15) from Daniel Suteu, Dec 05 2022
STATUS
approved