A262401 - OEIS

%I #29 Nov 16 2024 06:30:27

%S 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,

%T 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,

%U 56,27,18,9,60,6,6,63,64,15,6,7,28,9,70,7,72,7,14

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

%H Reinhard Zumkeller, <a href="/A262401/b262401.txt">Table of n, a(n) for n = 1..10000</a>

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

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

%F a(n) <= n.

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

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

%F A006530(a(n)) <= 7.

%F a(a(n)) = a(n).

%t Array[Times @@ (Power[Max@ IntegerDigits[#1], #2] & @@@ FactorInteger[#]) &, 74] (* _Michael De Vlieger_, Jan 23 2022 *)

%o (Haskell)

%o a262401 = product . map a054055 . a027746_row'

%o (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

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

%K nonn,base,mult

%O 1,2

%A _Reinhard Zumkeller_, Sep 25 2015