OFFSET
1,1
COMMENTS
Each prime factor must appear exactly once in the sum.
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
EXAMPLE
30 is a term because its distinct prime factors are 2, 3 and 5, and 30 = 2^1 + 3^1 + 5^2 = 2^4 + 3^2 + 5^1.
42 is a term because its distinct prime factors are 2, 3 and 7, and 42 = 2^3 + 3^3 + 7^1 = 2^5 + 3^1 + 7^1.
60 is a term because its distinct prime factors are 2, 3 and 5, and 60 = 2^5 + 3^1 + 5^2.
MAPLE
filter:= proc(n) local P, S, p, i;
P:= numtheory:-factorset(n);
S:= mul(add(x^(p^i), i=1..floor(log[p](n))), p=P);
coeff(S, x, n) > 0
end proc:
select(filter, [$1..1000]); # Robert Israel, Dec 27 2023
PROG
(PARI) isok(n)={my(f=factor(n)[, 1], m=n-vecsum(f)); polcoef(prod(k=1, #f, my(c=f[k]); sum(j=1, logint(m+c, c), x^(c^j-c)) , 1 + O(x*x^m)), m)} \\ Andrew Howroyd, Oct 27 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Tanmaya Mohanty, Oct 27 2023
EXTENSIONS
Terms a(43) and beyond from Andrew Howroyd, Oct 27 2023
STATUS
approved