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A357769 Positive numbers with decimal expansion d_1, ..., d_w that are divisible by d_1 + ... + d_k for k = 1..w.

%I A357769 #14 Oct 17 2022 07:06:41
%S A357769 1,2,3,4,5,6,7,8,9,10,12,18,20,24,30,36,40,48,50,60,70,80,90,100,102,
%T A357769 108,110,112,114,120,126,132,140,150,156,180,190,200,204,210,216,220,
%U A357769 224,228,230,240,252,264,270,280,300,306,312,330,336,360,396,400
%N A357769 Positive numbers with decimal expansion d_1, ..., d_w that are divisible by d_1 + ... + d_k for k = 1..w.
%C A357769 Leading zeros are ignored (d_1 > 0).
%C A357769 In other words, this sequence corresponds to numbers that are divisible by the sum of digits of all their prefixes.
%C A357769 All terms belong to A005349 (Niven numbers), A034837 and to A328273.
%C A357769 If t is a term, then 10*t is also a term (see A356350 for the primitive terms).
%C A357769 Contains no odd terms > 9. Else, d_1 and all d_1 + ... + d_k for k = 2..w-1 would have to be odd, but then d_1 + ... + d_w would be even. - _Michael S. Branicky_, Oct 15 2022
%H A357769 <a href="/index/De#decimal_expansion">Index entries for sequences related to decimal expansion of n</a>
%e A357769 180 is a term as it is divisible by 1, 1+8 and 1+8+0.
%e A357769 111 is not a term as it is divisible by 1 and 1+1+1 but not by 1+1.
%t A357769 Select[Range@400, And @@ IntegerQ /@ (#/Accumulate@ IntegerDigits@ #) &] (* _Giovanni Resta_, Oct 15 2022 *)
%o A357769 (PARI) is(n, base=10) = { my (d=digits(n, base), s=0); for (k=1, #d, if (n % (s+=d[k]), return (0));); return (1); }
%o A357769 (Python)
%o A357769 def ok(n):
%o A357769     s = str(n); sk = int(s[0])
%o A357769     for k in range(len(s)-1):
%o A357769         if n%sk != 0: return False
%o A357769         sk += int(s[k+1])
%o A357769     return n%sk == 0
%o A357769 print([k for k in range(1, 401) if ok(k)]) # _Michael S. Branicky_, Oct 12 2022
%Y A357769 Cf. A005349, A034837, A259433, A328273, A356350.
%K A357769 nonn,base,easy
%O A357769 1,2
%A A357769 _Rémy Sigrist_, Oct 12 2022