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A158287 Composite RMS numbers: composite numbers c such that root mean square of divisors of c is an integer. 1
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 (list; graph; refs; listen; history; text; internal format)
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 integer.
MATHEMATICA
Select[Range[13*10^5], CompositeQ[#]&&IntegerQ[RootMeanSquare[Divisors[ #]]]&] (* Harvey P. Dale, Sep 23 2022 *)
CROSSREFS
Sequence in context: A159949 A158252 A236869 * A112245 A289339 A011817
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Mar 15 2009
STATUS
approved

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Last modified June 22 14:17 EDT 2024. Contains 373587 sequences. (Running on oeis4.)