A237929 - OEIS

%I #17 May 03 2024 21:49:09

%S 2,9,98,170,1274,4233,4345,7105,7625,14905,21385,30457,34945,66585,

%T 69874,77314,82946,98841,175354,177122,233090,236282,238017,263145,

%U 265225,295274,298082,322234,335793,336106

%N Numbers n such that (i) the sum of prime divisors of n (with repetition) is one less than the sum of prime divisors (with repetition) of n+1, and (ii) n and n+1 have the same number of prime divisors (with repetition).

%C The first term a(1)=2 is the only prime number in this sequence.

%H Abhiram R Devesh, <a href="/A237929/b237929.txt">Table of n, a(n) for n = 1..96049</a>

%e For n=98: prime factors = 2,7,7; sum of prime factors = 16; number of prime divisors = 3

%e For n+1=99: prime factors = 3,3,11; sum of prime factors = 17; number of prime divisors=3.

%t 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 *)

%o (Python)

%o ## sumdivisors(n) is a function that would return the sum of prime

%o ## divisors of n

%o ## numdivisors(n) is a function that would return the number of prime

%o ## divisors of n

%o i=2

%o while i < 100000:

%o ..sdi=sumdivisors(i)

%o ..sdip=sumdivisors(i+1)

%o ..ndi=numdivisors(i)

%o ..ndip=numdivisors(i+1)

%o ..if sdi==sdip-1 and ndi==ndip:

%o ....print i, i+1

%o ..i=i+1

%Y Cf. A001414, A006145 Ruth-Aaron numbers (1): sum of prime divisors of n = sum of prime divisors of n+1.

%Y Cf. A228126 Sum of prime divisors of n (with repetition) is one less than the sum of prime divisors (with repetition) of n+1.

%Y Cf. A045920 Numbers n such that factorizations of n and n+1 have same number of primes (including multiplicities).

%K nonn

%O 1,1

%A _Abhiram R Devesh_, Feb 16 2014