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A134603 Numbers (excluding primes and powers of primes) such that the square mean of their prime factors is an integer (where the square mean of c and d is sqrt((c^2+d^2)/2)). 2
119, 161, 351, 378, 455, 527, 595, 721, 845, 918, 959, 1045, 1081, 1241, 1265, 1323, 1375, 1547, 1615, 1792, 1855, 2047, 2145, 2175, 2345, 2457, 2645, 2665, 2737, 3281, 3367, 3509, 3713, 3835, 3887, 3995, 4207, 4305, 4347, 4625, 4633, 4655, 4681, 5000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Numbers included in A134600, but not in A025475. a(1)=119 is the minimal number with this property.

LINKS

Hieronymus Fischer, Table of n, a(n) for n = 1..10000

EXAMPLE

a(2) = 161, since 161 = 7*23 and sqrt((7^2+23^2)/2) = sqrt(289) = 17 is an integer.

a(4) = 378, since 378 = 2*3*3*3*7 and sqrt((2^2+3*3^2+7^2)/5) = sqrt(80/5) = 4 is an integer.

a(28519) = 114445555, since 114445555 = 5*7*41*173*461 and sqrt((5^2+7^2+41^2+173^2+461^2)/5) = sqrt(48841) = 221.

CROSSREFS

Cf. A001597, A025475, A134333, A134344, A134376.

Cf. A134600, A134605, A134608, A134611, A134617, A134619, A134621.

Sequence in context: A135716 A026049 A247137 * A134604 A255580 A227515

Adjacent sequences:  A134600 A134601 A134602 * A134604 A134605 A134606

KEYWORD

nonn

AUTHOR

Hieronymus Fischer, Nov 11 2007

EXTENSIONS

Minor edits by the author, Apr 21 2013

STATUS

approved

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Last modified August 27 21:58 EDT 2015. Contains 261098 sequences.