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

1,3

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

Formula

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

Mathematica

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

Prog

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

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.

Sequence in context: A349608 A224709 A309965 * A070172 A273353 A367410

Adjacent sequences: A366382 A366383 A366384 * A366386 A366387 A366388

Keyword

nonn

Author

Antti Karttunen, Oct 23 2023

Status

approved