OFFSET
1,1
COMMENTS
The corresponding primes are 2, 3, 2, 5, 13, 5, 5, 7, 3, 11, 41, 11, 89, 2, 5, 37, 19, 13, 53, 37, ...
a(n) is a power of 2 for n = 1, 2, 4, 8, 12, 18, ... with the corresponding primes 2, 3, 5, 7, 11, 13, ...
a(n) is a perfect square for n = 1, 2, 3, 4, 8, 12, 14, 17, 18, ... with the corresponding primes 2, 3, 2, 5, 7, 11, 2, 19, 13, ...
EXAMPLE
64 is in the sequence because the divisors of 64 are {1, 2, 4, 8, 16, 32, 64} and 1/2 + 2/4 + 4/8 + 8/16 + 16/32 + 32/64 = 3 is prime.
MATHEMATICA
Do[s=0; Do[s=s+Divisors[n][[i]]/Divisors[n][[i+1]], {i, 1, Length[Divisors[n]]-1}]; If[PrimeQ[s]&&!PrimeQ[n], Print[n]], {n, 10^6}]
Select[Range[40000], PrimeQ[Total[#[[1]]/#[[2]]&/@Partition[ Divisors[ #], 2, 1]]]&] (* The program generates the first 10 terms of the sequence. To generate more, increase the Range constant. *) (* Harvey P. Dale, Feb 06 2022 *)
PROG
(Python)
from sympy import isprime, divisors
from fractions import Fraction
def ok(n):
divs = divisors(n)
f = sum(Fraction(dn, dd) for dn, dd in zip(divs[:-1], divs[1:]))
return f.denominator == 1 and isprime(f.numerator)
print([k for k in range(1, 40000) if ok(k)]) # Michael S. Branicky, Feb 06 2022
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Michel Lagneau, Feb 25 2015
EXTENSIONS
a(20) inserted and a(22)-a(23) from Michael S. Branicky, Feb 06 2022 using A227993
STATUS
approved