A122380 Numbers k such that k^2 > P(k)!, where P(k) is the greatest prime factor of k.
2, 3, 4, 6, 8, 9, 12, 15, 16, 18, 20, 24, 25, 27, 30, 32, 36, 40, 45, 48, 50, 54, 60, 64, 72, 75, 80, 81, 84, 90, 96, 98, 100, 105, 108, 112, 120, 125, 126, 128, 135, 140, 144, 147, 150, 160, 162, 168, 175, 180, 189, 192, 196, 200, 210, 216, 224, 225, 240, 243, 245
Offset: 1
Keywords
Examples
15^2 = 225 > 120 = 5! = P(15)!, so 15 is a member.
Links
- Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
- J. Sondow, A geometric proof that e is irrational and a new measure of its irrationality, Amer. Math. Monthly 113 (2006) 637-641.
- J. Sondow, A geometric proof that e is irrational and a new measure of its irrationality, arXiv:0704.1282 [math.HO], 2007-2010.
- J. Sondow and E. W. Weisstein, MathWorld: Smarandache Function
- Index entries for sequences related to factorial numbers.
Programs
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Mathematica
Reap[For[n = 2, n <= 250, n++, If[n^2 > FactorInteger[n][[-1, 1]]!, Print[n]; Sow[n]]]][[2, 1]] (* Jean-François Alcover, Feb 04 2019 *)
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PARI
smooth(P:vec, lim)=my(v=List([1]), nxt=vector(#P, i, 1), indx, t); while(1, t=vecmin(vector(#P, i, v[nxt[i]]*P[i]), &indx); if(t>lim, break); if(t>v[#v], listput(v, t)); nxt[indx]++); Vec(v) list(lim)=my(v=List([2]),u,lower,upper=2,p=2); while(1, lower=upper+1; p=nextprime(p+1); upper=min(sqrtint(p!), lim); if(lower>lim, break); u=select(q->q>=lower, smooth(primes([2,p-1]),upper)); for(i=1,#u, listput(v,u[i]))); Vec(v) \\ Charles R Greathouse IV, Nov 09 2021
Comments