A067552 - OEIS

%I #18 Feb 05 2021 05:30:26

%S 0,0,0,0,9,18,27,36,54,72,0,0,0,0,9,27,36,45,72,90,0,0,0,9,18,36,45,

%T 63,81,108,0,0,18,18,36,54,63,81,108,135,9,9,18,27,45,72,90,108,135,

%U 162,18,27,36,45,63,90,108,126,153,180,27,36,45,54,81,108,126,144,180,207

%N a(n) = SumOfDigits(n)^2 - SumOfDigits(n^2), where SumOfDigits = A007953.

%C All terms are divisible by 9; see A069912 for the quotient. - _Ivan Neretin_, Sep 01 2016

%H Ivan Neretin, <a href="/A067552/b067552.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) = A007953(n)^2 - A004159(n).

%e a(16) = SumOfDigits(16)^2 - SumOfDigits(16^2) = (1+6)^2 - SumOfDigits(256) = 7^2 - (2+5+6) = 49 - 13 = 36.

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

%o (PARI) a(n) = sumdigits(n)^2 - sumdigits(n^2); \\ _Michel Marcus_, Sep 01 2016

%Y Cf. A004159, A007953, A061909.

%K nonn,base

%O 0,5

%A _Reinhard Zumkeller_, Jan 28 2002

%E Edited by _Robert G. Wilson v_, May 04 2002