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

460, 99905, 463326, 808208947, 23089262218, 12442607161209225, 53780356630, 700326051644920151, 46634399568693102, 45573558879962759570353

Offset

3,1

Links

Table of n, a(n) for n=3..12.

Eric Weisstein's World of Mathematics, Centered Polygonal Number

Eric Weisstein's World of Mathematics, Distinct Prime Factors

Example

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.

Prog

(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

Crossrefs

Cf. A001221, A358862, A358863, A358864, A358865.

Sequence in context: A329292 A252535 A264242 * A107973 A227994 A142832

Adjacent sequences: A358891 A358892 A358893 * A358895 A358896 A358897

Keyword

nonn,more

Author

Ilya Gutkovskiy, Dec 05 2022

Extensions

a(8)-a(9) from Daniel Suteu, Dec 05 2022

a(10)-a(12) from Daniel Suteu, Dec 06 2022

Status

approved