A262401 In prime factorization of n: replace each factor with its largest decimal digit.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 12, 3, 14, 15, 16, 7, 18, 9, 20, 21, 2, 3, 24, 25, 6, 27, 28, 9, 30, 3, 32, 3, 14, 35, 36, 7, 18, 9, 40, 4, 42, 4, 4, 45, 6, 7, 48, 49, 50, 21, 12, 5, 54, 5, 56, 27, 18, 9, 60, 6, 6, 63, 64, 15, 6, 7, 28, 9, 70, 7, 72, 7, 14

Offset: 1

Author

Reinhard Zumkeller, Sep 25 2015

Keywords

• nonn
• base
• mult

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A054055, A027746, A001222, A002473, A006530, A060418, A068191.

Programs

Haskell

a262401 = product . map a054055 . a027746_row'

Mathematica

Array[Times @@ (Power[Max@ IntegerDigits[#1], #2] & @@@ FactorInteger[#]) &, 74] (* Michael De Vlieger, Jan 23 2022 *)

PARI

a(n) = my(f=factor(n)); for (k=1, #f~, f[k,1] = vecmax(digits(f[k,1]))); factorback(f); \\ Michel Marcus, Jan 22 2022

Formula

Multiplicative with p -> A054055(p), p prime.

a(n) = Product_{k=1..A001222(n)} A054055(A027746(n,k)).

a(n) <= n.

a(m) = m iff m is 7-smooth:

a(A002473(n)) = A002473(n) and a(A068191(n)) < A068191(n).

A006530(a(n)) <= 7.

a(a(n)) = a(n).