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A140172
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Powerful happy numbers; if a prime p divides n then p^2 must also divide n and also n must have trajectory under iteration of sum of squares of digits map includes 1.
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2
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1, 32, 49, 100, 392, 784, 1000, 1125, 1152, 1323, 1444, 1521, 3200, 3364, 3456, 4096, 4225, 4356, 4563, 4900, 7225, 7744, 8281, 8748, 9604, 10000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| For n=10^x such that x is an integer greater than 1, n is both powerful and happy.
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LINKS
| Index entries for sequences related to powerful numbers
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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
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CROSSREFS
| Cf. A001694, A007770.
Sequence in context: A043982 A045023 A066472 * A037008 A099048 A176542
Adjacent sequences: A140169 A140170 A140171 * A140173 A140174 A140175
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KEYWORD
| base,nonn
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AUTHOR
| Robin James Kerrison (rjk1994(AT)googlemail.com), Jun 22 2008
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