A335603 a(n) = p*q where p is the sequential number (or PrimePi, A000720) of the largest prime divisor of n, and q is the maximal exponent in the canonical representation of n (A051903).

0, 1, 2, 2, 3, 2, 4, 3, 4, 3, 5, 4, 6, 4, 3, 4, 7, 4, 8, 6, 4, 5, 9, 6, 6, 6, 6, 8, 10, 3, 11, 5, 5, 7, 4, 4, 12, 8, 6, 9, 13, 4, 14, 10, 6, 9, 15, 8, 8, 6, 7, 12, 16, 6, 5, 12, 8, 10, 17, 6, 18, 11, 8, 6, 6, 5, 19, 14, 9, 4, 20, 6, 21, 12, 6, 16, 5, 6, 22, 12

Offset: 1

Author

Todor Szimeonov, Jun 11 2020

Keywords

• nonn

Comments

a(n) is like a real-valued footprint of n.

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000720, A006530, A051903.

A076526 is a similar "footprint" of n.

Programs

Maple

with(numtheory):
a:= n-> pi(max(factorset(n)))*max(0, seq(i[2], i=ifactors(n)[2])):
seq(a(n), n=1..100);  # Alois P. Heinz, Jun 11 2020

Mathematica

a[n_] := PrimePi[(f = FactorInteger[n])[[-1, 1]]] * Max[f[[;; , 2]]]; Array[a, 100] (* Amiram Eldar, Jun 11 2020 *)

PARI

a(n) = if (n==1, 0, my(f=factor(n)); primepi(vecmax(f[, 1]))*vecmax(f[, 2])); \\ Michel Marcus, Jun 11 2020

Formula

a(n) = A000720(A006530(n)) * A051903(n). - Alois P. Heinz, Jun 11 2020

Extensions

Edited by N. J. A. Sloane, Jun 15 2020