A069234 Numbers k such that the sum over the prime divisors of k equals the number of divisors of k.

2, 9, 84, 126, 135, 196, 264, 294, 375, 468, 567, 594, 625, 1040, 1100, 1232, 1368, 1824, 2028, 2052, 2420, 2704, 2720, 3042, 3400, 4416, 6050, 6125, 7203, 7986, 8019, 8500, 8512, 8575, 8664, 8928, 9200, 9234, 11560, 13020, 16065, 16250, 19305

Offset

1,1

Comments

For distinct primes p,q, includes p^a*q^b if (a+1)*(b+1)=p+q. - Robert Israel, Jan 05 2018

Links

Robert Israel, Table of n, a(n) for n = 1..1000

Formula

k such that A000005(k) = A008472(k).

Maple

filter:= n -> numtheory:-tau(n)=convert(numtheory:-factorset(n), `+`):
select(filter, [$1..10^5]); # Robert Israel, Jan 05 2018

Mathematica

Select[Range[20000], Plus @@ ((f = FactorInteger[#])[[;; , 1]]) == Times @@ (f[[;; , 2]] + 1) &] (* Amiram Eldar, Jun 06 2022 *)

Crossrefs

Cf. A000005, A008472.

Sequence in context: A323769 A354045 A296581 * A086929 A193466 A354310

Adjacent sequences: A069231 A069232 A069233 * A069235 A069236 A069237

Keyword

easy,nonn

Author

Benoit Cloitre, Apr 13 2002

Status

approved