A358926 a(n) is the smallest centered n-gonal number with exactly n prime factors (counted with multiplicity).

316, 1625, 456, 3964051, 21568, 6561, 346528, 3588955448828761, 1684992, 210804461608463437, 36865024, 835904150390625, 2052407296

Offset: 3

Author

Ilya Gutkovskiy, Dec 06 2022

Keywords

• nonn
• more

Examples

			a(3) = 316, because 316 is a centered triangular number with 3 prime factors (counted with multiplicity) {2, 2, 79} and this is the smallest such number.
		

Links

• Eric Weisstein's World of Mathematics, Centered Polygonal Number
• Eric Weisstein's World of Mathematics, Prime Factor

Crossrefs

Cf. A001222, A358862, A358863, A358864, A358865, A358894, A358929.

Programs

Mathematica

c[n_, k_] := n*k*(k + 1)/2 + 1; a[n_] := Module[{k = 1, ck}, While[PrimeOmega[ck = c[n, k]] != n, k++]; ck]; Array[a, 7, 3] (* Amiram Eldar, Dec 09 2022 *)

PARI

a(n) = if(n<3, return()); for(k=1, oo, my(t=((n*k*(k+1))/2+1)); if(bigomega(t) == n, return(t))); \\ Daniel Suteu, Dec 09 2022

Extensions

a(10)-a(15) from Daniel Suteu, Dec 09 2022