A334128 Integers m such that sigma(m) + sigma(7*m) = 16*m.

135, 1365, 42819777

Offset

1,1

Comments

This is the case h = 7 of the h-perfect numbers as defined in the Harborth link.

If gcd(m, 7) = 1 and m is even, then m must be of the form 2*q, where 27*sigma(q) = 32*q and gcd(q, 7) = 1.

a(4) > 3.5*10^12, if it exists. - Giovanni Resta, May 17 2020

Links

Table of n, a(n) for n=1..3.

Heiko Harborth, On h-perfect numbers, Annales Mathematicae et Informaticae, 41 (2013) pp. 57-62.

Prog

(PARI) isok(m) = sigma(m) + sigma(7*m) == 16*m;

Crossrefs

Cf. A000203, A000396, A281993, A330412, A330413.

Sequence in context: A238330 A358002 A157734 * A210102 A061073 A195671

Adjacent sequences: A334125 A334126 A334127 * A334129 A334130 A334131

Keyword

nonn,bref,hard,more

Author

Jinyuan Wang, May 15 2020

Status

approved