cp's OEIS Frontend

A237929 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).

%I A237929 #22 Aug 08 2025 10:29:08
%S A237929 2,9,98,170,1274,4233,4345,7105,7625,14905,21385,30457,34945,66585,
%T A237929 69874,77314,82946,98841,175354,177122,233090,236282,238017,263145,
%U A237929 265225,295274,298082,322234,335793,336106
%N A237929 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 A237929 The first term a(1)=2 is the only prime number in this sequence.
%H A237929 Abhiram R Devesh, <a href="/A237929/b237929.txt">Table of n, a(n) for n = 1..96049</a>
%e A237929 For n=98: prime factors = 2,7,7; sum of prime factors = 16; number of prime divisors = 3
%e A237929 For n+1=99: prime factors = 3,3,11; sum of prime factors = 17; number of prime divisors=3.
%t A237929 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 A237929 (Python)
%o A237929 from sympy import primeomega
%o A237929 def is_A237929(n): return A001414(n) == A001414(n+1)-1 and primeomega(n) == primeomega(n+1) # _David Radcliffe_, Aug 08 2025
%Y A237929 Cf. A001414, A006145 Ruth-Aaron numbers (1): sum of prime divisors of n = sum of prime divisors of n+1.
%Y A237929 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 A237929 Cf. A045920 Numbers n such that factorizations of n and n+1 have same number of primes (including multiplicities).
%K A237929 nonn
%O A237929 1,1
%A A237929 _Abhiram R Devesh_, Feb 16 2014