A324710 Number x such that x = Sum_{i=1..k}{sigma(x/p_i)}, where p_i are the k prime factors of x.

1748, 5588, 138128, 1683728, 9286208, 12642368, 152287808, 447483968

Offset

1,1

Comments

All the terms appear to be multiples of 4.

a(9) > 2*10^11. Up to a(8) all the terms are of the form 2^k * p * q, with p and q primes. The next such terms in the sequence are 2^16*197539*41626667, 2^16*196817*183392089, and 2^20*3360697*49177969. - Giovanni Resta, Mar 14 2019

Links

Table of n, a(n) for n=1..8.

Example

Prime factors of 1748 are 2, 19, 23 and sigma(1748/2) + sigma(1748/19) + sigma(1748/23) = 1440 + 168 + 140 = 1748.

Maple

with(numtheory): P:=proc(q) local k, n; for n from 1 to q do
if n=add(sigma(n/k), k=factorset(n)) then print(n);
fi; od; end: P(10^9);

Prog

(PARI) isok(x) = my(f=factor(x)[, 1]~); x == sum(k=1, #f, sigma(x/f[k])); \\ Michel Marcus, Mar 15 2019

Crossrefs

Cf. A000203, A324711.

Sequence in context: A190829 A038010 A362875 * A201801 A172833 A172882

Adjacent sequences: A324707 A324708 A324709 * A324711 A324712 A324713

Keyword

nonn,hard,more

Author

Paolo P. Lava, Mar 13 2019

Extensions

a(7)-a(8) from Giovanni Resta, Mar 14 2019

Status

approved