A158287 Composite RMS numbers: composite numbers c such that root mean square of divisors of c is an integer.

287, 1673, 3055, 6665, 9545, 9799, 9855, 21385, 26095, 34697, 46655, 66815, 68593, 68985, 125255, 155287, 182665, 242879, 273265, 380511, 391345, 404055, 421655, 627215, 730145, 814463, 823537, 876785, 1069895, 1087009, 1166399, 1204281, 1256489, 1289441

Offset: 1

Author

Jaroslav Krizek, Mar 15 2009

Keywords

• nonn

Comments

a(n) = composite number c (A002808), iff sqrt(sigma_2(c)/tau(c)) = sqrt(A001157(c)/A000005(c)) = k, for k = natural numbers (A000027). Prime RMS numbers (NSW primes) in A088165.

16 of the first 1654 terms are even (the smallest is 2217231104). The first 16 even terms are all divisible by 30976. - Donovan Johnson, Apr 17 2013

Examples

			a(1) = 287, sqrt(A001157(287)/A000005(287)) = sqrt(84100/4) = 145, number 145 is an integer.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..7424 (terms < 10^13, first 1654 terms from Donovan Johnson)

Crossrefs

Cf. A001157, A000005, A088165, A140480.

Programs

Mathematica

Select[Range[13*10^5],CompositeQ[#]&&IntegerQ[RootMeanSquare[Divisors[ #]]]&] (* Harvey P. Dale, Sep 23 2022 *)