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).

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, 36, 0, 6, 12, 18, 24, 30, 36, 42, 48, 54, 0, 8, 16, 24, 32, 40, 48, 56, 64, 72, 0, 10, 20, 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

Offset: 0

Author

Amarnath Murthy, Sep 25 2003

Keywords

• base
• easy
• nonn

Comments

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).

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

Examples

			a(1234) = 234 + 2*134 + 3*124 + 4*123 = 1366.
		

Links

• Jinyuan Wang, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A069816, A087346, A088117.

Programs

Mathematica

Join[{0},Table[Total[IntegerDigits[n]Table[FromDigits[Drop[ IntegerDigits[ n],{d}]],{d,IntegerLength[n]}]],{n,100}]] (* Harvey P. Dale, Dec 23 2021 *)

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

Extensions

More terms from David Wasserman, May 10 2005

Offset 0 from Stéphane Rézel, Jul 31 2019