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

1,1

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

Links

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

Example

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

Mathematica

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

Crossrefs

Cf. A001157, A000005, A088165, A140480.

Sequence in context: A159949 A158252 A236869 * A112245 A289339 A011817

Adjacent sequences: A158284 A158285 A158286 * A158288 A158289 A158290

Keyword

nonn

Author

Jaroslav Krizek, Mar 15 2009

Status

approved