A076526 - OEIS

A076526

a(n) = r * max(e_1, ..., e_r), where n = p_1^e_1 . .... p_r^e_r is the canonical prime factorization of n, a(1) = 0.

0, 1, 1, 2, 1, 2, 1, 3, 2, 2, 1, 4, 1, 2, 2, 4, 1, 4, 1, 4, 2, 2, 1, 6, 2, 2, 3, 4, 1, 3, 1, 5, 2, 2, 2, 4, 1, 2, 2, 6, 1, 3, 1, 4, 4, 2, 1, 8, 2, 4, 2, 4, 1, 6, 2, 6, 2, 2, 1, 6, 1, 2, 4, 6, 2, 3, 1, 4, 2, 3, 1, 6, 1, 2, 4, 4, 2, 3, 1, 8, 4, 2, 1, 6, 2, 2, 2, 6, 1, 6, 2, 4, 2, 2, 2, 10, 1, 4, 4, 4, 1, 3, 1, 6, 3

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OFFSET

1,4

COMMENTS

Introduced by Luis Flavio Soares Nunes - see link. Omega(n) <= a(n) for n > 1, where Omega(n) = the number of prime factors of n, counting multiplicity, A001222.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10000

Carlos Rivera, Puzzle #201 The Arithmetic Function A(n) in "The Prime Puzzles and Problems Connection".

Index entries for sequences computed from exponents in factorization of n.

FORMULA

a(n) = A001221(n) * A051903(n). - Antti Karttunen, May 28 2017

MATHEMATICA

a[n_] := Module[{pf}, pf = Transpose[FactorInteger[n]]; Length[pf[[1]]]*Max[pf[[2]]]]; Table[a[i], {i, 2, 100}]

PROG

(PARI) a(n) = if(n == 1, 0, my(e = factor(n)[, 2]); vecmax(e) * #e); \\ Amiram Eldar, Sep 08 2024

CROSSREFS

Cf. A001221, A001222, A051903, A076558, A076745.