OFFSET

1,2

COMMENTS

For n=10^x such that x is an integer greater than 1, n is both powerful and happy.

LINKS

EXAMPLE

2 --> 4 --> 16 --> 37 --> ... --> 4, which repeats with period 8, so never reaches 1, so 2 (and 4, 16 etc.) are unhappy.

7 --> 7^2=49 --> 4^2+9^2=97 --> 9^2+7^2=130 --> 1^2+3^2+0^2=10 --> 1^2+0^2=1

However, 7 divides by 7 and not 7^2.

32 --> 3^2+2^2=13 --> 1^2+3^2=10 --> 1^2+0^2=1

and 32 divides by 2 (and no other prime number) and by 2^2. So 32 is powerful and happy

CROSSREFS

KEYWORD

base,nonn

AUTHOR

Robin James Kerrison (rjk1994(AT)googlemail.com), Jun 22 2008

STATUS

approved