A087141 Numbers divisible by the sum of their digits, but not by all their individual digits.

10, 18, 20, 21, 27, 30, 40, 42, 45, 50, 54, 60, 63, 70, 72, 80, 81, 84, 90, 100, 102, 108, 110, 114, 117, 120, 133, 140, 150, 152, 153, 156, 171, 180, 190, 192, 195, 198, 200, 201, 204, 207, 209, 210, 220, 225, 228, 230, 234, 240, 243, 247, 252, 261, 266, 270

Offset: 1

Author

Reinhard Zumkeller, Aug 18 2003

Keywords

• nonn
• base

Examples

			225 is in the sequence as 225 is divisible by 2 + 2 + 5 = 9 but not by 2 while 2 is a digit of 225. - _David A. Corneth_, Jan 28 2021
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000

Crossrefs

Intersection of A087140 and A005349.

Cf. A087142.

Programs

PARI

is(n) = { my(d = digits(n), sd = vecsum(d), s = Set(d)); if(sd != 0 && n % sd == 0, if(s[1] == 0, return(1) ); for(i = 1, #s, if(n % s[i] != 0, return(1) ) ); 0 ); 0 } \\ David A. Corneth, Jan 28 2021

Python

def ok(n):
    d = list(map(int, str(n)))
    if n == 0 or n%sum(d): return False
    return 0 in d or any(n%di for di in set(d))
print([k for k in range(271) if ok(k)]) # Michael S. Branicky, Oct 18 2021