

A354563


Numbers k such that P(k)^2  k and P(k+1)^3  (k+1), where P(k) = A006530(k) is the largest prime dividing k.


5



242, 2400, 6859, 10647, 47915, 57121, 344604, 499999, 830465, 1012499, 1431125, 2098853, 2825760, 2829123, 3930399, 5560691, 11859210, 12323584, 13137830, 18253460, 18279039, 21093749, 30664296, 32279841, 33999932, 37218852, 38640401, 38740085, 41485688, 45222737
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OFFSET

1,1


LINKS



EXAMPLE

242 = 2 * 11^2 is a term since P(242) = 11 and 11^2  242, 243 = 3^5, P(243) = 3, and 3^3  243.


MATHEMATICA

p[n_] := FactorInteger[n][[1, 2]]; Select[Range[10^6], p[#] > 1 && p[# + 1] > 2 &]


PROG

(Python)
from sympy import factorint
def c(n, e): f = factorint(n); return f[max(f)] >= e
def ok(n): return n > 1 and c(n, 2) and c(n+1, 3)


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



