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A366914
Numbers expressible as the sum of their distinct prime factors raised to a natural exponent.
2
2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, 23, 25, 27, 29, 30, 31, 32, 37, 41, 42, 43, 47, 49, 53, 59, 60, 61, 64, 67, 70, 71, 73, 79, 81, 83, 84, 89, 90, 97, 101, 102, 103, 107, 109, 113, 121, 125, 127, 128, 131, 132, 137, 139, 140, 149, 150, 151, 157, 163, 167
OFFSET
1,1
COMMENTS
Each prime factor must appear exactly once in the sum.
LINKS
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
Sequence in context: A326848 A328957 A030230 * A089352 A086486 A071139
KEYWORD
nonn
AUTHOR
Tanmaya Mohanty, Oct 27 2023
EXTENSIONS
Terms a(43) and beyond from Andrew Howroyd, Oct 27 2023
STATUS
approved