A224988 Even RMS numbers: even numbers n such that root mean square of divisors of n is an integer.

2217231104, 6221622528, 9644780288, 12127073024, 15377570560, 15520617728, 22426778880, 25138541824, 34766068480, 43551357696, 49424655104, 56022543104, 67513462016, 84107119360, 84889511168, 90906475264, 107642993920, 156987452160, 174347951360, 175969792768

Offset: 1

Author

Donovan Johnson, Apr 25 2013

Keywords

• nonn

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

Examples

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

Links

• Giovanni Resta, Table of n, a(n) for n = 1..83 (terms < 10^13)
• Donovan Johnson, 177 terms > 2*10^11

Crossrefs

Cf. A000005, A001157, A140480.

Programs

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

Formula

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