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 A284342 Numbers n such that A065642(n) < n*lpf(n), where lpf = least prime factor (A020639). 5
 12, 18, 24, 36, 40, 45, 48, 50, 54, 56, 60, 63, 72, 75, 80, 84, 90, 96, 98, 100, 108, 112, 120, 126, 132, 135, 144, 147, 150, 156, 160, 162, 168, 175, 176, 180, 189, 192, 196, 198, 200, 204, 208, 216, 224, 225, 228, 234, 240, 242, 245, 250, 252, 264, 270, 275, 276, 280, 288, 294, 297, 300 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Numbers n for which A065642(n) < A285109(n). Positions of terms > 1 in A285337. - Antti Karttunen, Apr 19 2017 For any n in this sequence, k*n is also in this sequence. No term is squarefree. For any distinct primes p and q with p > q, p^2*q and p*q^(ceiling(log_q(p))) are in this sequence. - Charlie Neder, Oct 29 2018 LINKS Antti Karttunen, Table of n, a(n) for n = 1..10000 MATHEMATICA Select[Range[2, 300], Function[{n, c, lpf}, SelectFirst[Range[n + 1, n^2], Times @@ FactorInteger[#][[All, 1]] == c &] < n lpf] @@ {#1, Times @@ #2, #2[[1]]} & @@ {#, FactorInteger[#][[All, 1]]} &] (* Michael De Vlieger, Oct 31 2018 *) PROG (PARI) for(n=1, 300, for(k=1, n^2-n, a=factorback(factorint(n)[, 1]); b=factorback(factorint(n+k)[, 1]); c=vecmin(factor(n)[, 1]); if(a==b&&n+k r, n = n+r); n); }; isA284342(n) = (A065642(n) < n*A020639(n)); n=0; k=1; while(k <= 10000, n=n+1; if(isA284342(n), write("b284342.txt", k, " ", n); k=k+1)); \\ Antti Karttunen, Apr 19 2017 (Python) from operator import mul from sympy import primefactors from functools import reduce def a007947(n): return 1 if n<2 else reduce(mul, primefactors(n)) def a065642(n): if n==1: return 1 r=a007947(n) n = n + r while a007947(n)!=r: n+=r return n print([n for n in range(10, 301) if a065642(n)

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Last modified September 29 02:18 EDT 2023. Contains 365748 sequences. (Running on oeis4.)