cp's OEIS Frontend

A366914 Numbers expressible as the sum of their distinct prime factors raised to a natural exponent.

%I A366914 #24 Dec 27 2023 14:31:01
%S A366914 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,
%T A366914 53,59,60,61,64,67,70,71,73,79,81,83,84,89,90,97,101,102,103,107,109,
%U A366914 113,121,125,127,128,131,132,137,139,140,149,150,151,157,163,167
%N A366914 Numbers expressible as the sum of their distinct prime factors raised to a natural exponent.
%C A366914 Each prime factor must appear exactly once in the sum.
%H A366914 Robert Israel, <a href="/A366914/b366914.txt">Table of n, a(n) for n = 1..10000</a>
%e A366914 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.
%e A366914 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.
%e A366914 60 is a term because its distinct prime factors are 2, 3 and 5, and 60 = 2^5 + 3^1 + 5^2.
%p A366914 filter:= proc(n) local P,S,p,i;
%p A366914   P:= numtheory:-factorset(n);
%p A366914   S:= mul(add(x^(p^i),i=1..floor(log[p](n))),p=P);
%p A366914   coeff(S,x,n) > 0
%p A366914 end proc:
%p A366914 select(filter, [$1..1000]); # _Robert Israel_, Dec 27 2023
%o A366914 (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
%K A366914 nonn
%O A366914 1,1
%A A366914 _Tanmaya Mohanty_, Oct 27 2023
%E A366914 Terms a(43) and beyond from _Andrew Howroyd_, Oct 27 2023