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

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, 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, 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

Offset: 1

Author

Antti Karttunen, Oct 25 2022

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences computed from exponents in factorization of n
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A046523, A056239, A355930.

Programs

Maple

a:= n-> (l-> add(i*l[i][2], i=1..nops(l)))
        (sort(ifactors(n)[2], (x, y)->x[2]>y[2])):
seq(a(n), n=1..105);  # Alois P. Heinz, Oct 26 2022

Mathematica

{0}~Join~Array[Total@ MapIndexed[#1 First[#2] &, Sort[FactorInteger[#][[All, -1]], Greater]] &, 120] (* Michael De Vlieger, Oct 25 2022 *)

PARI

A356159(n) = A056239(A046523(n));
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
A056239(n) = { my(f); if(1==n, 0, f=factor(n); sum(i=1, #f~, f[i, 2] * primepi(f[i, 1]))); }

Formula

a(n) = A056239(A046523(n)).