A082939 Numbers such that sum of the digits of the product of the factorial of digits of the number is equal to the sum of the digits of the number.

1, 2, 10, 18, 20, 22, 27, 36, 63, 72, 81, 100, 108, 114, 117, 126, 135, 141, 153, 162, 171, 180, 200, 202, 207, 216, 220, 261, 270, 306, 315, 333, 351, 360, 411, 513, 531, 603, 612, 621, 630, 702, 711, 720, 801, 810, 1000, 1008, 1014, 1017, 1026, 1035, 1041

Offset: 1

Author

Meenakshi Srikanth (menakan_s(AT)yahoo.com), Apr 27 2003

Keywords

• nonn
• base

Examples

			63 = 6!*3! = 720*6 = 4320, 4 + 3 + 2 + 0 = 9 and 6 + 3 = 9.
		

References

• Suggested by Amarnath Murthy.

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A007953, A066459, A082940.

Programs

Python

from math import factorial, prod
def ok(n):
    d = list(map(int, str(n)))
    return sum(map(int, str(prod(map(factorial, d))))) == sum(d)
print([k for k in range(1042) if ok(k)]) # Michael S. Branicky, Aug 15 2022

Formula

Numbers k such that A007953(k) = A007953(A066459(k)).

Extensions

Corrected and extended by Jason Earls, May 22 2004