cp's OEIS Frontend

A088116 Let n = abc..., where a, b, c, are digits of n. a(n) = a*bc...+b*ac...+c*ab...+..., i.e., a(n) = sum, over all the digits, of the product (number obtained by deleting a digit multiplied by the deleted digit).

%I A088116 #30 Dec 23 2021 18:32:05
%S A088116 0,0,0,0,0,0,0,0,0,0,0,2,4,6,8,10,12,14,16,18,0,4,8,12,16,20,24,28,32,
%T A088116 36,0,6,12,18,24,30,36,42,48,54,0,8,16,24,32,40,48,56,64,72,0,10,20,
%U A088116 30,40,50,60,70,80,90,0,12,24,36,48,60,72,84,96,108,0,14,28,42,56,70,84,98
%N A088116 Let n = abc..., where a, b, c, are digits of n. a(n) = a*bc...+b*ac...+c*ab...+..., i.e., a(n) = sum, over all the digits, of the product (number obtained by deleting a digit multiplied by the deleted digit).
%C A088116 First 100 terms (for all two digit numbers) match with that of A069816. A088116(10a + b) = 2ab = (a+b)^2 - (a^2 + b^2) = A069816(10a + b).
%C A088116 The first known fixed points, after zero, are numbers of the forms 36*10^k and 1314*10^k for k >= 0. All have 9 as the sum of their digits. Calculated up to n = 10^10. - _Stéphane Rézel_, Jul 31 2019
%H A088116 Jinyuan Wang, <a href="/A088116/b088116.txt">Table of n, a(n) for n = 0..10000</a>
%e A088116 a(1234) = 234 + 2*134 + 3*124 + 4*123 = 1366.
%t A088116 Join[{0},Table[Total[IntegerDigits[n]Table[FromDigits[Drop[ IntegerDigits[ n],{d}]],{d,IntegerLength[n]}]],{n,100}]] (* _Harvey P. Dale_, Dec 23 2021 *)
%o A088116 (PARI) a(n) = {v=digits(n);sum(k=1,#v,v[k]*(n\10^(#v-k+1)*10^(#v-k)+n%10^(#v-k)));} \\ _Jinyuan Wang_, Aug 01 2019
%Y A088116 Cf. A069816, A087346, A088117.
%K A088116 base,easy,nonn
%O A088116 0,12
%A A088116 _Amarnath Murthy_, Sep 25 2003
%E A088116 More terms from _David Wasserman_, May 10 2005
%E A088116 Offset 0 from _Stéphane Rézel_, Jul 31 2019