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

1,2

Links

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

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).

Mathematica

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

Prog

(Haskell)
a262401 = product . map a054055 . a027746_row'
(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

Crossrefs

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

Sequence in context: A360074 A280505 A375968 * A118541 A084905 A180409

Adjacent sequences: A262398 A262399 A262400 * A262402 A262403 A262404

Keyword

nonn,base,mult

Author

Reinhard Zumkeller, Sep 25 2015

Status

approved