A232445 Numbers n such that sigma(n) and sigma(n^2) are squares.

1, 11177320, 182937066, 159839399818, 166474679436

Offset: 1

Author

Alex Ratushnyak, Nov 24 2013

Keywords

• nonn
• hard
• more

Comments

Intersection of A006532 and A008847.

sigma(a(6)) >= 10^12. - Hiroaki Yamanouchi, Sep 26 2014

Examples

			sigma(a(2)) = (64*9*5*2)^2 and sigma(a(2)^2) = (3*7*13*19*31*127)^2.
sigma(a(3)) = (64*9*5*7)^2 and sigma(a(3)^2) = (3*7*13*37*61*499)^2.
sigma(a(4)) = (256*9*5*47)^2 and sigma(a(4)^2) = (3*49*13*19*37*43*61*67)^2.
sigma(a(5)) = (16*3*7*121*17)^2 and sigma(a(5)^2) = (3*49*13*31*61*109*757)^2.
		

Crossrefs

Cf. A000203 (sigma: sum of divisors of n), A006532, A008847, A232444.

Programs

PARI

isok(n) = issquare(sigma(n)) && issquare(sigma(n^2)); \\ Michel Marcus, Sep 24 2014

Extensions

a(4) from Hiroaki Yamanouchi, Sep 24 2014

a(5) from Hiroaki Yamanouchi, Sep 26 2014