Original entry on oeis.org
27, 125, 147, 539, 2197, 2992, 3159, 3249, 3757, 4199, 4851, 5733, 6517, 11774, 15717, 16807, 19652, 20475, 25289, 28899, 30625, 31213, 31465, 33275, 34122, 41327, 43384, 44616, 50255, 60858, 61250, 61750, 62271
Offset: 1
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Flatten@ Values@ Map[Rest, Rest@ PositionIndex@ Array[Times @@ Select[Prime@ Range[#1, #1 + #2], Function[p, p <= #3]] & @@ {PrimePi@ NextPrime[FactorInteger[#][[-1, 1]]], PrimePi@ #, #} &, 10^4]] (* Michael De Vlieger, Nov 03 2017 *)
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upto(n) = {my(l = List(), p = 3, res = List, c); forprime(q = 5, nextprime(n + 1), for(i = p + 1, q - 1, f = factor(i)[, 1]; listput(l, [f[#f], precprime(i), i])); p = q); listsort(l); i = 1; while(i < #l - 1, if(l[i][1] == l[i+1][1], if(l[i][2] == l[i+1][2], listput(res, l[i+1][3]))); i++); listsort(res); res} \\ David A. Corneth, Nov 03 2017
A137799
Consider the first run of composites that contains at least two numbers whose largest prime factor is prime(n), n >= 2. a(n) is the first of these numbers.
Original entry on oeis.org
24, 120, 140, 528, 2184, 2975, 3230, 50232, 11745, 15686, 62234, 265639, 171957, 34075, 1133405, 2313685, 1060790, 332320, 1334161, 404858, 1388504, 1357216, 15800704, 5516293, 66896037, 11962832, 6084983, 129761775, 43216511, 90972513
Offset: 2
The composites between 23 and 29 form the first run containing two numbers with largest prime factor prime(2) = 3, viz. 24 = 2*2*2*3 and 27 = 3*3*3. Hence a(2) = 24.
The composites between 2313679 and 2313767 form the first run containing two numbers with largest prime factor prime(17) = 59, viz. 2313685 = 5*11*23*31*59 and 2313744 = 2*2*2*2*3*19*43*59. Hence a(17) = 2313685.
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{m=30; v=vector(m); w=v; p=3; c=0; while(cb&&f[matsize(f)[1], 1]<=p&&g[matsize(g)[1], 1]<=p); c++; v[c]=a; w[c]=b; p=nextprime(p+1)); print("A137799:"); print(v); print("A137800:"); print(w)} /* Klaus Brockhaus, Feb 15 2008 */
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10 'puzzle 430 (duplicate prime factors) 20 N=2313680 30 A=1:S=N\2:print N; 40 B=N\A 50 if B*A=N and B=prmdiv(B) and B<=S then print B;:goto 80 60 A=A+1 70 if A<=N\2 then 40 80 C=C+1:print C: if B=59 then T=T+1 81 if N=2313700 then stop 90 if T=2 then T=0:stop 100 N=N+1: if N=prmdiv(N) then C=0:T=0:stop:print:goto 100:else 30
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