OFFSET
1,1
COMMENTS
The first term a(1)=2 is the only prime number in this sequence.
LINKS
Abhiram R Devesh, Table of n, a(n) for n = 1..96049
EXAMPLE
For n=98: prime factors = 2,7,7; sum of prime factors = 16; number of prime divisors = 3
For n+1=99: prime factors = 3,3,11; sum of prime factors = 17; number of prime divisors=3.
MATHEMATICA
Select[Partition[Table[{n, PrimeOmega[n], Total[Times@@@FactorInteger[n]]}, {n, 34*10^4}], 2, 1], #[[1, 2]]==#[[2, 2]]&&#[[1, 3]]+1==#[[2, 3]]&][[;; , 1, 1]] (* Harvey P. Dale, May 03 2024 *)
PROG
(Python)
## sumdivisors(n) is a function that would return the sum of prime
## divisors of n
## numdivisors(n) is a function that would return the number of prime
## divisors of n
i=2
while i < 100000:
..sdi=sumdivisors(i)
..sdip=sumdivisors(i+1)
..ndi=numdivisors(i)
..ndip=numdivisors(i+1)
..if sdi==sdip-1 and ndi==ndip:
....print i, i+1
..i=i+1
CROSSREFS
Cf. A001414, A006145 Ruth-Aaron numbers (1): sum of prime divisors of n = sum of prime divisors of n+1.
Cf. A228126 Sum of prime divisors of n (with repetition) is one less than the sum of prime divisors (with repetition) of n+1.
Cf. A045920 Numbers n such that factorizations of n and n+1 have same number of primes (including multiplicities).
KEYWORD
nonn
AUTHOR
Abhiram R Devesh, Feb 16 2014
STATUS
approved