cp's OEIS Frontend

A356159 Sum of the prime indices of the smallest number that has the same prime signature as n.

%I A356159 #13 Oct 30 2022 23:05:35
%S A356159 0,1,1,2,1,3,1,3,2,3,1,4,1,3,3,4,1,4,1,4,3,3,1,5,2,3,3,4,1,6,1,5,3,3,
%T A356159 3,6,1,3,3,5,1,6,1,4,4,3,1,6,2,4,3,4,1,5,3,5,3,3,1,7,1,3,4,6,3,6,1,4,
%U A356159 3,6,1,7,1,3,4,4,3,6,1,6,4,3,1,7,3,3,3,5,1,7,3,4,3,3,3,7,1,4,4,6,1,6,1,5,6
%N A356159 Sum of the prime indices of the smallest number that has the same prime signature as n.
%H A356159 Antti Karttunen, <a href="/A356159/b356159.txt">Table of n, a(n) for n = 1..65537</a>
%H A356159 <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>
%H A356159 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A356159 a(n) = A056239(A046523(n)).
%p A356159 a:= n-> (l-> add(i*l[i][2], i=1..nops(l)))
%p A356159         (sort(ifactors(n)[2], (x, y)->x[2]>y[2])):
%p A356159 seq(a(n), n=1..105);  # _Alois P. Heinz_, Oct 26 2022
%t A356159 {0}~Join~Array[Total@ MapIndexed[#1 First[#2] &, Sort[FactorInteger[#][[All, -1]], Greater]] &, 120] (* _Michael De Vlieger_, Oct 25 2022 *)
%o A356159 (PARI)
%o A356159 A356159(n) = A056239(A046523(n));
%o A356159 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
%o A356159 A056239(n) = { my(f); if(1==n, 0, f=factor(n); sum(i=1, #f~, f[i, 2] * primepi(f[i, 1]))); }
%Y A356159 Cf. A046523, A056239, A355930.
%K A356159 nonn
%O A356159 1,4
%A A356159 _Antti Karttunen_, Oct 25 2022