

A140172


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.


3



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, 10125, 10976, 11025, 12167, 12321, 12348, 12996, 13824, 14112, 14283, 14641, 15625, 17424, 17672, 17956
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OFFSET

1,2


COMMENTS

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


LINKS

Donovan Johnson, Table of n, a(n) for n = 1..1000
Index entries for sequences related to powerful numbers


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

Cf. A001694, A007770.
Sequence in context: A222300 A259770 A066472 * A259765 A256521 A037008
Adjacent sequences: A140169 A140170 A140171 * A140173 A140174 A140175


KEYWORD

base,nonn


AUTHOR

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


STATUS

approved



