OFFSET
1,2
COMMENTS
Define n as a 'psigma perfect number' if psigma(n) = 2n. 18 is a psigma perfect number. The p sigma divisors are 1,2,6,9 and 18 and the sum = 36. Conjecture: 18 is the only psigma perfect number.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
EXAMPLE
a(30) = 1 + 2 + 6 + 30 = 39. The divisors 3, 5, 10 and 15 are not considered for the sum as 3 and 5 have the same prime signature as 2 and also 10 and 15 have the same prime signature as 6.
MATHEMATICA
a[n_] := Module[{d = Rest[Divisors[n]]}, 1 + Total@DeleteDuplicatesBy[{#, Sort[FactorInteger[#][[;; , 2]]]} & /@ d, Last][[;; , 1]]]; Array[a, 71] (* Amiram Eldar, Jul 20 2019 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Amarnath Murthy, Jul 21 2003
EXTENSIONS
More terms from David Wasserman, Mar 07 2005
STATUS
approved