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

1,4

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

Formula

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

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 *)

Prog

(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]))); }

Crossrefs

Cf. A046523, A056239, A355930.

Sequence in context: A329616 A304795 A036459 * A377247 A294926 A079167

Adjacent sequences: A356156 A356157 A356158 * A356160 A356161 A356162

Keyword

nonn

Author

Antti Karttunen, Oct 25 2022

Status

approved