A224977 n^2 minus sum of digits of n^2.

0, 0, 0, 0, 9, 18, 27, 36, 54, 72, 99, 117, 135, 153, 180, 216, 243, 270, 315, 351, 396, 432, 468, 513, 558, 612, 657, 711, 765, 828, 891, 945, 1017, 1071, 1143, 1215, 1278, 1350, 1431, 1512, 1593, 1665, 1746, 1827, 1917, 2016, 2106, 2196, 2295, 2394, 2493

Offset: 0

Author

Kevin L. Schwartz and Christian N. K. Anderson, Apr 21 2013

Keywords

• nonn
• base
• easy

Comments

a(n) mod 9 = 0 for all n.

Examples

			a(0) = 0^2 - 0 = 0.
a(12) = 144 - (1+4+4) = 135.
		

Links

• Christian N. K. Anderson, Table of n, a(n) for n = 0..9999
• Christian N. K. Anderson, Ulam spiral of a(n) in red, with other multiples of 9 in gray.

Crossrefs

Cf. A067552.

Derived from A000290 and A004159.

Programs

Mathematica

Table[n^2 - Sum[DigitCount[n^2][[i]]i, {i, 9}], {n, 50}] (* Alonso del Arte, Apr 21 2013 *)
#^2-Total[IntegerDigits[#^2]]&/@Range[0,50] (* Harvey P. Dale, May 10 2017 *)

R

library(gmp); digsum<-function(x) sum(as.numeric(unlist(strsplit(as.character(x),split=""))))
ans=rep(0,100); n=0
while(n<=100) ans[(n=n+1)]=n^2-digsum(n^2); ans

Formula

a(n) = A000290(n) - A004159(n).