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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<n*c&!print1(n", ")&break)))

(PARI)

A020639(n) = if(1==n, n, vecmin(factor(n)[, 1]));

A007947(n) = factorback(factorint(n)[, 1]); \\ From Andrew Lelechenko, May 09 2014

A065642(n) = { my(r=A007947(n)); if(1==n, n, n = n+r; while(A007947(n) <> 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

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 xrange(10, 301) if a065642(n)<n*min(primefactors(n))] # Indranil Ghosh, Apr 20 2017

CROSSREFS

Cf. A007947, A020639, A065642, A285100 (complement), A285109, A285337.

Sequence in context: A241852 A113756 A055482 * A198470 A245379 A224218

Adjacent sequences:  A284339 A284340 A284341 * A284343 A284344 A284345

KEYWORD

nonn

AUTHOR

Gionata Neri, Mar 25 2017

STATUS

approved

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Last modified March 22 17:25 EDT 2019. Contains 321422 sequences. (Running on oeis4.)