Integer Sequence "sums of digits of squares".

elementary-number-theory recurrence-relations

$\delta(9)=9$, $\delta(99)=18$, $\delta(999)=27$, etc., shows you get every number with digital root 0.

$\delta(49)=7$, $\delta(499)=16$, $\delta(4999)=25$, etc, shows you get every number with digital root 7.

$\delta(8)=10$, $\delta(98)=19$, $\delta(998)=28$, etc., shows you get every number with digital root 1.

$\delta(7)=13$, $\delta(97)=22$, $\delta(997)=31$, etc., finishes the problem off.

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