A371278 Numbers k > 1 such that k / A054841(k) is an integer.

2, 4, 12, 16, 144, 192, 256, 1728, 3888, 4320, 6480, 7200, 11520, 13122, 14580, 15360, 20736, 36864, 49152, 65536, 107520, 344064, 384000, 589824, 691200, 1244160, 1259712, 1327104, 2211840, 2304960, 2963520, 2985984, 3932160, 3981312, 4478976, 4500000

Offset: 1

Author

Ctibor O. Zizka, Mar 17 2024

Keywords

• nonn

Examples

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

Crossrefs

Cf. A054841, A001146 (a subsequence).

Programs

Mathematica

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 *)

Python

from sympy import factorint, primepi
def ok(n): return n > 1 and n%sum(e*10**(primepi(p)-1) for p, e in factorint(n).items()) == 0
print([k for k in range(10**4) if ok(k)]) # Michael S. Branicky, Mar 17 2024

Extensions

More terms from Michel Marcus, Mar 17 2024