

A286302


Numbers n such that A133364(n) <= 1.


0



1, 2, 3, 4, 5, 7, 8, 9, 10, 13, 16, 17, 22, 24, 25, 26, 31, 36, 58, 64, 76, 82, 120, 170, 193, 196, 214, 324, 328, 370, 412, 562, 676, 730, 10404
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OFFSET

1,2


COMMENTS

Numbers n such that there is at most one representation n = m+p with m in A001694 and p prime.
There are no more terms <= 10^7.
The only n <= 10^7 for which A133364(n) = 0 are 1, 2, and 5.
Conjecture: 10404 is the last term.


LINKS

Table of n, a(n) for n=1..35.
Math Overflow, Is every powerful number the sum of a powerful number and a prime?.


MAPLE

N:= 10^7: # to get all terms <= N
q:= proc(x, N) local p, R;
R:= {x};
for p in numtheory:factorset(x) do
R:= map(t > seq(t*p^i, i=0..floor(log[p](N/t))), R)
od;
R
end proc:
Pow:= `union`(seq(q(n^2, N), n=1..isqrt(N))):
Primes:= select(isprime, [2, seq(i, i=3..N, 2)]):
CPow:= Vector(N): CPow[convert(Pow, list)]:= 1:
CPrimes:= Vector(N): CPrimes[Primes]:= 1:
Conv:= SignalProcessing:Convolution(CPow, CPrimes):
select(t > Conv[t1] < 1.5, [$2..N]);


CROSSREFS

Cf. A001694, A133364.
Sequence in context: A230999 A180590 A289342 * A299767 A129268 A271317
Adjacent sequences: A286299 A286300 A286301 * A286303 A286304 A286305


KEYWORD

nonn


AUTHOR

Robert Israel, May 05 2017


STATUS

approved



