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 A359235 a(n) is the smallest centered square number with exactly n prime factors (counted with multiplicity). 1
 1, 5, 25, 925, 1625, 47125, 2115625, 4330625, 83760625, 1049140625, 6098828125, 224991015625, 3735483578125, 329495166015625, 8193863401953125, 7604781494140625, 216431299462890625, 148146624615478515625, 25926420587158203125, 11071085186929931640625 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS a(14) <= 33811910869140625, a(15) <= 7604781494140625, a(16) <= 216431299462890625. - Robert Israel, Dec 22 2022 LINKS Table of n, a(n) for n=0..19. Eric Weisstein's World of Mathematics, Centered Square Number Eric Weisstein's World of Mathematics, Prime Factor EXAMPLE a(4) = 1625, because 1625 is a centered square number with 4 prime factors (counted with multiplicity) {5, 5, 5, 13} and this is the smallest such number. MAPLE cs:= n -> 2*n*(n+1)+1: V:= Vector(12): count:= 0: for n from 1 while count < 12 do v:= cs(n); w:= numtheory:-bigomega(v); if V[w] = 0 then V[w]:= v; count:= count+1 fi od: convert(V, list); # Robert Israel, Dec 22 2022 PROG (PARI) bigomega_centered_square_numbers(A, B, n) = A=max(A, 2^n); (f(m, p, n) = my(list=List()); if(n==1, forprime(q=max(p, ceil(A/m)), B\m, if(q%4==1, my(t=m*q); if(issquare(2*t-1), listput(list, t)))), forprime(q=p, sqrtnint(B\m, n), if(q%4==1, my(t=m*q); if(ceil(A/t) <= B\t, list=concat(list, f(t, q, n-1)))))); list); vecsort(Vec(f(1, 2, n))); a(n) = if(n==0, return(1)); my(x=2^n, y=2*x); while(1, my(v=bigomega_centered_square_numbers(x, y, n)); if(#v >= 1, return(v[1])); x=y+1; y=2*x); \\ Daniel Suteu, Dec 29 2022 CROSSREFS Cf. A001222, A001844, A358926, A358929, A359234. Sequence in context: A279835 A169652 A359232 * A137114 A067212 A061583 Adjacent sequences: A359232 A359233 A359234 * A359236 A359237 A359238 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Dec 22 2022 EXTENSIONS a(11)-a(13) from Robert Israel, Dec 22 2022 a(14)-a(19) from Daniel Suteu, Dec 29 2022 STATUS approved

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Last modified September 7 23:52 EDT 2024. Contains 375749 sequences. (Running on oeis4.)