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A224988 Even RMS numbers: even numbers n such that root mean square of divisors of n is an integer. 2
2217231104, 6221622528, 9644780288, 12127073024, 15377570560, 15520617728, 22426778880, 25138541824, 34766068480, 43551357696, 49424655104, 56022543104, 67513462016, 84107119360, 84889511168, 90906475264, 107642993920, 156987452160, 174347951360, 175969792768 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Even numbers from A140480.

The first 20 terms are all divisible by 30976. 30976 = 2^8*11^2.

a(21) > 2*10^11.

All the 83 terms up to 10^13 are divisible by 30976. - Giovanni Resta, Oct 29 2019

LINKS

Giovanni Resta, Table of n, a(n) for n = 1..83 (terms < 10^13)

Donovan Johnson, 177 terms > 2*10^11

FORMULA

Even numbers n such that A001157(n)/A000005(n) is a square.

EXAMPLE

n = 2217231104 (even). sigma_2(n) = 6616291782395055852. n has 108 divisors. 6616291782395055852/108 = 247511537^2.

PROG

(PARI) forstep(n=2, 10^10, 2, s=sigma(n, 2); nd=numdiv(n); if(s%nd==0, if(issquare(s\nd), print(n))))

(PARI) isok(n) = my(s=sigma(n, 2), nd=numdiv(n)); if(s%nd==0, issquare(s\nd), 0); \\ program adapted by Michel Marcus, Oct 29 2019

CROSSREFS

Cf. A000005, A001157, A140480.

Sequence in context: A017604 A288080 A274366 * A327056 A180688 A225760

Adjacent sequences:  A224985 A224986 A224987 * A224989 A224990 A224991

KEYWORD

nonn

AUTHOR

Donovan Johnson, Apr 25 2013

STATUS

approved

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Last modified April 3 14:34 EDT 2020. Contains 333197 sequences. (Running on oeis4.)