login
A086469
Sum of the distinct (smallest) prime signature divisors of n. In case of two or more divisors with the same prime signature the smallest is considered to evaluate the sum. Let this function be defined as psigma(n).
3
1, 3, 4, 7, 6, 9, 8, 15, 13, 13, 12, 25, 14, 17, 19, 31, 18, 36, 20, 37, 25, 25, 24, 57, 31, 29, 40, 49, 30, 39, 32, 63, 37, 37, 41, 61, 38, 41, 43, 85, 42, 51, 44, 73, 73, 49, 48, 121, 57, 88, 55, 85, 54, 117, 61, 113, 61, 61, 60, 115, 62, 65, 97, 127, 71, 75, 68, 109, 73, 83, 72
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
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
Cf. A086470.
Sequence in context: A351923 A341944 A332994 * A087030 A175187 A332993
KEYWORD
nonn
AUTHOR
Amarnath Murthy, Jul 21 2003
EXTENSIONS
More terms from David Wasserman, Mar 07 2005
STATUS
approved