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

135, 1365, 42819777

Offset: 1

Author

Jinyuan Wang, May 15 2020

Keywords

• nonn
• bref
• hard
• more

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

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

Crossrefs

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

Programs

PARI

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