A023651 Numbers k such that (product of digits of k) * (sum of digits of k) = 2k.

0, 2, 15, 24, 1575, 39366

Offset: 1

Author

Jason Earls, Dec 11 2001

Keywords

• nonn
• base
• fini
• full

Comments

Except for k = 0, this sequence is a subsequence of A049101. - Jason Yuen, Feb 26 2024

Crossrefs

Cf. A007953, A007954, A049101.

Cf. A038364, A038369, A062237, A066282.

Programs

Mathematica

Do[ If[ 2n == Apply[ Times, IntegerDigits[n]] Apply[ Plus, IntegerDigits[n]], Print[n]], {n, 0, 10^7} ]

PARI

isok(n) = if(n, factorback(digits(n)), 0) * sumdigits(n) == 2*n \\ Mohammed Yaseen, Jul 22 2022

Python

from math import prod
def s(n): return sum(map(int, str(n)))
def p(n): return prod(map(int, str(n)))
for n in range(0, 10**6):
  if p(n)*s(n)==2*n:
    print(n) # Mohammed Yaseen, Jul 22 2022

Extensions

Offset corrected by Arkadiusz Wesolowski, Oct 17 2012