A359961
Smallest Zuckerman number (A007602) with exactly n distinct prime factors.
Original entry on oeis.org
1, 2, 6, 132, 3276, 27132, 1117116, 111914712, 6111417312, 1113117121116, 1112712811322112, 11171121131111172
Offset: 0
3276 = 2^2*3^2*7*13 is the smallest integer with 4 distinct prime factors that is also Zuckerman number as 3276 / (3*2*7*6) = 13, so a(4) = 3276.
A095224
Least squarefree Fibonacci number with exactly n prime divisors.
Original entry on oeis.org
1, 2, 21, 610, 6765, 701408733, 102334155, 190392490709135, 251728825683549488150424261, 23416728348467685, 13598018856492162040239554477268290, 81055900096023504197206408605
Offset: 0
a(5) = 701408733 = 3 * 43 * 89 * 199 * 307.
-
From R. J. Mathar, Oct 14 2010: (Start)
A001221 := proc(n) nops(numtheory[factorset](n)) ; end proc:
A095224 := proc(n) for i from 1 do f := combinat[fibonacci](i) ; if A001221(f) =n and numtheory[bigomega](f) = n then return f ; fi; od ; end proc:
for n from 1 do printf("%d,\n",A095224(n)) ; end do: (End)
-
Table[SelectFirst[{#,PrimeOmega[#]}&/@Select[Fibonacci[Range[200]],SquareFreeQ],#[[2]] == n&],{n,0,11}][[;;,1]] (* Harvey P. Dale, Mar 06 2024 *)
a(9) corrected and 3 terms added by
R. J. Mathar, Oct 14 2010
A360301
Smallest exclusionary square (A029783) with exactly n distinct prime factors.
Original entry on oeis.org
2, 18, 84, 858, 31122, 3383898, 188841114, 68588585868, 440400004044, 7722272777722272
Offset: 1
84 = 2^2 * 3 * 7 is the smallest integer with 3 distinct prime factors that is also an exclusionary square, because 84^2 = 7056, so a(3) = 84.
858 = 2 * 3 * 11 * 13 is the smallest integer with 4 distinct prime factors that is also an exclusionary square, because 858^2 = 736164, so a(4) = 858.
- Clifford A. Pickover, A Passion for Mathematics, Wiley, 2005; see p. 60.
- David Wells, The Penguin Dictionary of Curious and Interesting Numbers, Revised Edition, 1997, page 144, entry 567.
-
omega_exclusionary_squares(A, B, n) = A=max(A, vecprod(primes(n))); (f(m, p, j) = my(list=List()); forprime(q=p, sqrtnint(B\m, j), if(q == 5, next); my(v=m*q); while(v <= B, if(j==1, if(v>=A && #setintersect(Set(digits(v)), Set(digits(v^2))) == 0, listput(list, v)), if(v*(q+1) <= B, list=concat(list, f(v, q+1, j-1)))); v *= q)); list); vecsort(Vec(f(1, 2, n)));
a(n) = my(x=vecprod(primes(n)), y=2*x); while(1, my(v=omega_exclusionary_squares(x, y, n)); if(#v >= 1, return(v[1])); x=y+1; y=2*x); \\ Daniel Suteu, Feb 05 2023
Comments