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A358894 a(n) is the smallest centered n-gonal number with exactly n distinct prime factors.

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%I A358894 #12 Feb 16 2025 08:34:04
%S A358894 460,99905,463326,808208947,23089262218,12442607161209225,53780356630,
%T A358894 700326051644920151,46634399568693102,45573558879962759570353
%N A358894 a(n) is the smallest centered n-gonal number with exactly n distinct prime factors.
%H A358894 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CenteredPolygonalNumber.html">Centered Polygonal Number</a>
%H A358894 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DistinctPrimeFactors.html">Distinct Prime Factors</a>
%e A358894 a(3) = 460, because 460 is a centered triangular number with 3 distinct prime factors {2, 5, 23} and this is the smallest such number.
%o A358894 (PARI) a(n) = if(n<3, return()); for(k=1, oo, my(t=((n*k*(k+1))/2+1)); if(omega(t) == n, return(t))); \\ _Daniel Suteu_, Dec 05 2022
%Y A358894 Cf. A001221, A358862, A358863, A358864, A358865.
%K A358894 nonn,more
%O A358894 3,1
%A A358894 _Ilya Gutkovskiy_, Dec 05 2022
%E A358894 a(8)-a(9) from _Daniel Suteu_, Dec 05 2022
%E A358894 a(10)-a(12) from _Daniel Suteu_, Dec 06 2022