A395529 - OEIS

%I #28 May 17 2026 20:04:47

%S 1,479,958,1559,1679,1916,2297,2419,2927,2971,2999,3071,3118,3358,

%T 3499,3733,3832,4309,4594,4677,4793,4838,5037,5461,5539,5683,5711,

%U 5854,5942,5998,6043,6142,6236,6998,7321,7466,7531,7619,7669,7795,7981,8191,8399,8618,8711,8909

%N Numbers k such that k cannot be written as m + t where m*t belongs to A055932.

%C Also numbers k such that k^2 - 4*t is never a square for any t in A055932. - _David A. Corneth_, May 12 2026

%H David A. Corneth, <a href="/A395529/b395529.txt">Table of n, a(n) for n = 1..10000</a> (first 267 terms from Zhicheng Wei)

%p filter:= proc(k) local m,v,F;

%p   for m from 1 to k/2 do

%p     v:= m*(k-m);

%p     F:= NumberTheory:-PrimeFactors(v);

%p     if NumberTheory:-pi(max(F)) = nops(F) then return false fi;

%p   od;

%p true

%p end proc:

%p filter(2):= false:

%p select(filter, [$1..10000]); # _Robert Israel_, Apr 27 2026

%o (PARI)

%o A055932(n)=my(f=factor(n)[, 1]~); f==primes(#f)

%o is(n)=sum(k=1,n/2,A055932(k*(n-k)))==0

%o select(is, [1..4000])

%o (Python)

%o from itertools import count, islice

%o from sympy import primefactors, prime

%o def A395529_gen(startvalue=1): # generator of terms >= startvalue

%o     for k in count(max(startvalue,1)):

%o         for m in range(1,k):

%o             p = set(primefactors(m))|set(primefactors(k-m))

%o             if (l:=len(p)) == 0 or prime(l) == max(p):

%o                 break

%o         else:

%o             yield k

%o A395529_list = list(islice(A395529_gen(),50)) # _Chai Wah Wu_, Apr 27 2026

%Y Cf. A055932.

%K nonn,easy

%O 1,2

%A _Zhicheng Wei_, Apr 27 2026