A062043 Positive numbers whose product of digits is 10 times their sum.

459, 495, 549, 594, 945, 954, 1566, 1656, 1665, 2259, 2295, 2355, 2529, 2535, 2553, 2592, 2925, 2952, 3255, 3525, 3552, 5166, 5229, 5235, 5253, 5292, 5325, 5352, 5523, 5532, 5616, 5661, 5922, 6156, 6165, 6516, 6561, 6615, 6651, 9225, 9252, 9522

Offset: 1

Author

Amarnath Murthy, Jun 28 2001

Keywords

• nonn
• base
• easy

Comments

A subsequence of A011535 as each term must include the digit 5. - Chai Wah Wu, Dec 09 2015

Examples

			594 belongs to the sequence as (5*9*4)/(5+9+4) = 180/18 = 10.
		

Links

• Harry J. Smith, Table of n, a(n) for n = 1..500

Crossrefs

Cf. A011540, A034710, A062034, A062035, A062036, A062382, A062037, A062384, A062040, A062041, A062045.

Cf. A011535, A124694.

Programs

Maple

filter:= proc(t) local L;
  L:= convert(t,base,10);
  convert(L,`*`) = 10*convert(L,`+`)
end proc:
select(filter, [$1..10^5]); # Robert Israel, Sep 11 2022

Mathematica

Select[Range[10000], Times @@ IntegerDigits[ # ] == 10 Plus @@ IntegerDigits[ # ] &] (* Tanya Khovanova, Dec 25 2006 *)

PARI

isok(n) = my(d=digits(n)); vecprod(d)==10*vecsum(d) \\ Mohammed Yaseen, Sep 11 2022

Python

from math import prod
def ok(n): d = list(map(int, str(n))); return prod(d) == 10*sum(d)
print([k for k in range(1, 9999) if ok(k)]) # Michael S. Branicky, Sep 11 2022

Extensions

More terms from Harvey P. Dale and Larry Reeves (larryr(AT)acm.org), Jul 06 2001