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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 21 22:32 EDT 2019. Contains 326169 sequences. (Running on oeis4.)