cp's OEIS Frontend

A176194 Numbers with no zero digits divisible by the sum of the k-th powers of their digits, for each k = 1,2,3,4.

%I A176194 #11 Apr 20 2023 04:22:23
%S A176194 1,111,1121211,11243232,12132432,12413232,22331232,23111352,23411232,
%T A176194 24113232,41223312,42131232,44662464,111111111,112452144,114251424,
%U A176194 135964224,211412544,246134592,313212312,332131212,382941675,416283624,442114512,523173456,671635575,979652772
%N A176194 Numbers with no zero digits divisible by the sum of the k-th powers of their digits, for each k = 1,2,3,4.
%C A176194 For the numbers divisible by the sum of k-th powers of digits including 0, see A169662. The numbers such that the digits are > 0 are rare.
%H A176194 Amiram Eldar, <a href="/A176194/b176194.txt">Table of n, a(n) for n = 1..464</a>
%F A176194 A007953 (n)|n and A003132(n)|n and A055012 (n)| n and A055013 (n)| n and all digits < > 0.
%e A176194 For n = 246134592 we obtain :
%e A176194 2^4 + 4^4 + 6^4 + 1^4 + 3^4 + 4^4 + 5^4 + 9^4 + 2^4 = 9108, and 246134592 = 9108*27024 ;
%e A176194 2^3 + 4^3 + 6^3 + 1^3 + 3^3 + 4^3 + 5^3 + 9^3 + 2^3 = 1242, and 246134592 = 1242*198176 ;
%e A176194 2^2 + 4^2 + 6^2 + 1^2 + 3^2 + 4^2 + 5^2 + 9^2 + 2^2 = 192, and 246134592 = 192*1281951 ;
%e A176194 2 + 4 + 6 + 1 + 3 + 4 + 5 + 9 + 2 = 36, and 246134592 = 36*6837072.
%p A176194 with(numtheory):for n from 2 to 500000000 do:l:=evalf(floor(ilog10(n))+1):n0:=n:s1:=0:s2:=0:s3:=0:s4:=0:p:=1:for m from 1 to l do:q:=n0:u:=irem(q,10):v:=iquo(q,10):n0:=v :s1:=s1+u:p:=p*u:s2:=s2+u^2:s3:=s3+u^3:s4:=s4+u^4: od:if irem(n,s1)=0 and irem(n,s2)=0 and irem(n,s3)=0 and irem(n,s4)=0 and p<>0 then print(n):else fi:od:
%Y A176194 Intersection of A052382 and A169662.
%Y A176194 Cf. A034087, A072081, A117562, A034087, A072081, A117562, A034088, A034088.
%K A176194 nonn,base
%O A176194 1,2
%A A176194 _Michel Lagneau_, Apr 11 2010
%E A176194 a(1)-a(2) and more terms add by _Amiram Eldar_, Apr 20 2023