A291459 Numbers n having a proper divisor d such that sigma(n) - k*d = k*n. Case k = 5.

294053760, 575134560, 739458720, 882161280, 1193512320, 1314593280, 1725403680, 2539555200, 2588105520, 2646483840, 2711348640, 3008396160, 3891888000, 4053329280, 4214770560, 4648644000, 4802878080, 5176211040, 5194949760, 5258373120, 6470263800, 6768891360, 7900532640

Offset

1,1

Comments

Case k=2 are the admirable numbers (A111592).

Subset of A215264.

Links

Table of n, a(n) for n=1..23.

Example

One of the proper divisors of 294053760 is 2056320 and sigma(294053760) - 5*2056320 = 1480550400 - 10281600 = 1470268800 = 5*294053760.
One of the proper divisors of 3891888000 is 314496 and sigma(3891888000) - 5*314496 = 19461012480 - 1572480 = 19459440000 = 5*3891888000.

Maple

with(numtheory): P:=proc(q, h) local a, k, n; for n from 1 to q do a:=sort([op(divisors(n))]);
for k from 1 to nops(a)-1 do if sigma(n)-h*a[k]=h*n then print(n); break; fi; od; od; end: P(10^10, 5);

Crossrefs

Cf. A000203, A111592, A215264, A291457, A291458.

Sequence in context: A344648 A251566 A112452 * A034640 A186015 A183800

Adjacent sequences: A291456 A291457 A291458 * A291460 A291461 A291462

Keyword

nonn,easy

Author

Paolo P. Lava, Aug 24 2017

Status

approved