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Numbers k > 1 such that k / A054841(k) is an integer.
0

%I #23 Mar 19 2024 07:17:32

%S 2,4,12,16,144,192,256,1728,3888,4320,6480,7200,11520,13122,14580,

%T 15360,20736,36864,49152,65536,107520,344064,384000,589824,691200,

%U 1244160,1259712,1327104,2211840,2304960,2963520,2985984,3932160,3981312,4478976,4500000

%N Numbers k > 1 such that k / A054841(k) is an integer.

%e k = 144: A054841(144) = 24 because 144 = 3^2 * 2^4, 144/A054841(144) = 144/24 = 6, thus 144 is a term.

%t q[n_] := Module[{f = FactorInteger[n]}, Divisible[n, Total[10^(PrimePi[f[[;; , 1]]] - 1) * f[[;; , 2]]]]]; q[1] = False; Select[Range[10^5], q] (* _Amiram Eldar_, Mar 17 2024 *)

%o (Python)

%o from sympy import factorint, primepi

%o def ok(n): return n > 1 and n%sum(e*10**(primepi(p)-1) for p, e in factorint(n).items()) == 0

%o print([k for k in range(10**4) if ok(k)]) # _Michael S. Branicky_, Mar 17 2024

%Y Cf. A054841, A001146 (a subsequence).

%K nonn

%O 1,1

%A _Ctibor O. Zizka_, Mar 17 2024

%E More terms from _Michel Marcus_, Mar 17 2024