A366385 Divide n by its largest prime factor, then multiply with the index of that same prime; a(1) = 0 by convention.

0, 1, 2, 2, 3, 4, 4, 4, 6, 6, 5, 8, 6, 8, 9, 8, 7, 12, 8, 12, 12, 10, 9, 16, 15, 12, 18, 16, 10, 18, 11, 16, 15, 14, 20, 24, 12, 16, 18, 24, 13, 24, 14, 20, 27, 18, 15, 32, 28, 30, 21, 24, 16, 36, 25, 32, 24, 20, 17, 36, 18, 22, 36, 32, 30, 30, 19, 28, 27, 40, 20, 48, 21, 24, 45, 32, 35, 36, 22, 48, 54, 26, 23, 48, 35

Offset: 1

Author

Antti Karttunen, Oct 23 2023

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Index entries for sequences related to Matula-Goebel numbers
• Index entries for sequences related to prime indices in the factorization of n

Crossrefs

Cf. A000720, A006530, A052126, A061395.

Cf. A196050 (number of iterations needed to reach 1), A366388 (number of iterations to reach the nearest power of 2), A109129 (exponent of the nearest power of 2 reached).

Cf. also A366387, A324923.

Programs

Mathematica

Array[PrimePi[#2]*#1/#2 & @@ {#, FactorInteger[#][[-1, 1]]} &, 85] (* Michael De Vlieger, Oct 23 2023 *)

PARI

A006530(n) = if(1==n, n, my(f=factor(n)); f[#f~, 1]);
A366385(n) = { my(gpf=A006530(n)); primepi(gpf)*(n/gpf); };

Formula

a(n) = A052126(n)*A061395(n) = (n/A006530(n)) * A000720(A006530(n)).