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A361874
a(n) is the least k such that k, k+1 and 2*k+1 all have exactly n prime factors counted with multiplicity.
0
2, 25, 171, 1592, 37975, 928624, 8412687, 106390624, 2306890624, 37119730112, 429122890624, 23027923554687
OFFSET
1,1
COMMENTS
From Ray Chandler, Apr 08 2023: (Start)
a(13) <= 2088002787109375.
a(14) <= 7002191787109375.
a(15) <= 100007718212890624.
a(16) <= 4838361918212890624.
a(17) <= 86569490081787109375. (End)
From Ray Chandler, Apr 11 2023: (Start)
a(13) <= 1228742893554687.
a(15) <= 22134455942791167. (End)
EXAMPLE
a(3) = 171 because 171 = 3^2*19, 171 + 1 = 172 = 2^2*43, and 2*171 + 1 = 343 = 7^3 all have 3 prime factors, and 171 is the least number that works.
MAPLE
f:= proc(n) local x;
for x from 2^n do
if numtheory:-bigomega(x)=n and numtheory:-bigomega(x+1)=n and numtheory:-bigomega(2*x+1)=n then
return x
fi od end proc:
map(f, [$1..6]);
MATHEMATICA
a={}; nmax=6; For[n=1, n<=nmax, n++, For[k=1, k>0, k++, If[PrimeOmega[k]==PrimeOmega[k+1]==PrimeOmega[2k+1]==n, AppendTo[a, k]; k=-1]]]; a (* Stefano Spezia, Mar 31 2023 *)
PROG
(PARI) chk(k, n) = (bigomega(k)==n) && (bigomega(k+1)==n) && (bigomega(2*k+1)==n); \\ Michel Marcus, Apr 12 2023
CROSSREFS
Cf. A001222.
Sequence in context: A063264 A024533 A220276 * A215298 A094218 A203767
KEYWORD
nonn,more
AUTHOR
Zak Seidov and Robert Israel, Mar 27 2023
EXTENSIONS
a(11) from Michael S. Branicky, Mar 30 2023
a(12) from Martin Ehrenstein, Apr 12 2023
STATUS
approved