login
Numbers k such that k is congruent to the product of its digits modulo the sum of its digits.
1

%I #12 Jun 18 2018 04:01:32

%S 1,2,3,4,5,6,7,8,9,10,11,14,19,20,29,30,31,33,36,39,40,49,50,52,55,59,

%T 60,63,64,69,70,71,77,79,80,89,90,99,100,102,108,110,113,118,119,120,

%U 132,140,150,166,168,180,190,195,198,200,201,204

%N Numbers k such that k is congruent to the product of its digits modulo the sum of its digits.

%H Harry J. Smith, <a href="/A065448/b065448.txt">Table of n, a(n) for n = 1..1000</a>

%e 14 is in the sequence because 14 == 4 (mod 5).

%t Select[Range[2000], Mod[ # - Apply[Times, IntegerDigits[[ # ]]], Apply[Plus, IntegerDigits[[ # ]]]] == 0 &]

%o (PARI) SumD(x)= { local(s=0); while (x>9, s+=x-10*(x\10); x\=10); return(s + x) } ProdD(x)= { local(p=1); while (x>9 && p>0, p*=(x-10*(x\10)); x\=10); return(p*x) } { n=0; for (m=1, 10^9, p=ProdD(m); s=SumD(m); if ((m - p)%s == 0, write("b065448.txt", n++, " ", m); if (n==1000, return)) ) } \\ _Harry J. Smith_, Oct 19 2009

%Y Cf. A007953, A007954.

%K base,nonn

%O 1,2

%A _Santi Spadaro_, Nov 18 2001