A069816 a(n) = (sum of digits of n)^2 - (sum of digits^2 of n).

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

Offset: 0

Author

N. J. A. Sloane, May 03 2002

Keywords

• nonn
• base
• easy

Comments

a(n) = 0 iff n is a single-digit number or is a power of ten times a single-digit number. - Robert G. Wilson v, May 04 2002

Examples

			n=14: sum of digits = 5, squaring gives 25; sum of squared digits of n = 1^2 + 4^2 = 17, so a(14) = 25 - 17 = 8.
		

Crossrefs

Cf. A067552.

Programs

Maple

A007953 := proc(n) add(d, d=convert(n,base,10)) ; end proc: A003132:= proc(n) add(d^2, d=convert(n,base,10)) ; end proc: A118881 := proc(n) (A007953(n))^2 ; end proc: A069816 := proc(n) A118881(n)-A003132(n) ; end proc: seq(A069816(n),n=0..80) ; # R. J. Mathar, Jun 23 2009

Mathematica

f[n_] := Plus @@ IntegerDigits[n]^2 - Plus @@ (IntegerDigits[n]^2); Table[ f[n], {n, 0, 100}]

Formula

From R. J. Mathar, Jun 23 2009: (Start)

a(n) = 2*A035930(n), n <= 100.

a(n) = A118881(n) - A003132(n). (End)

Extensions

Extended by Robert G. Wilson v, May 04 2002