A395529 Numbers k such that k cannot be written as m + t where m*t belongs to A055932.

1, 479, 958, 1559, 1679, 1916, 2297, 2419, 2927, 2971, 2999, 3071, 3118, 3358, 3499, 3733, 3832, 4309, 4594, 4677, 4793, 4838, 5037, 5461, 5539, 5683, 5711, 5854, 5942, 5998, 6043, 6142, 6236, 6998, 7321, 7466, 7531, 7619, 7669, 7795, 7981, 8191, 8399, 8618, 8711, 8909

Offset

1,2

Comments

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

Links

David A. Corneth, Table of n, a(n) for n = 1..10000 (first 267 terms from Zhicheng Wei)

Maple

filter:= proc(k) local m, v, F;
  for m from 1 to k/2 do
    v:= m*(k-m);
    F:= NumberTheory:-PrimeFactors(v);
    if NumberTheory:-pi(max(F)) = nops(F) then return false fi;
  od;
true
end proc:
filter(2):= false:
select(filter, [$1..10000]); # Robert Israel, Apr 27 2026

Prog

(PARI)
A055932(n)=my(f=factor(n)[, 1]~); f==primes(#f)
is(n)=sum(k=1, n/2, A055932(k*(n-k)))==0
select(is, [1..4000])
(Python)
from itertools import count, islice
from sympy import primefactors, prime
def A395529_gen(startvalue=1): # generator of terms >= startvalue
    for k in count(max(startvalue, 1)):
        for m in range(1, k):
            p = set(primefactors(m))|set(primefactors(k-m))
            if (l:=len(p)) == 0 or prime(l) == max(p):
                break
        else:
            yield k
A395529_list = list(islice(A395529_gen(), 50)) # Chai Wah Wu, Apr 27 2026

Crossrefs

Cf. A055932.

Sequence in context: A056987 A323051 A025025 * A377476 A108256 A393084

Adjacent sequences: A395526 A395527 A395528 * A395530 A395531 A395532

Keyword

nonn,easy

Author

Zhicheng Wei, Apr 27 2026

Status

approved