A232445 - OEIS

A232445

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

1, 11177320, 182937066, 159839399818, 166474679436

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OFFSET

1,2

COMMENTS

Intersection of A006532 and A008847.

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

LINKS

EXAMPLE

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.

PROG

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

CROSSREFS

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

KEYWORD

nonn,hard,more

AUTHOR

EXTENSIONS

a(4) from Hiroaki Yamanouchi, Sep 24 2014

a(5) from Hiroaki Yamanouchi, Sep 26 2014

STATUS

approved