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A077655 Number of consecutive successors of n having the same number of prime factors as n (counted with multiplicity). 4

%I #9 Aug 01 2021 11:04:35

%S 0,1,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,1,0,1,0,0,0,0,0,2,1,

%T 0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,

%U 0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,2,1,0,0,0,0,0,0,2,1,0,0,0,1,0,0,0,0,0,0,0

%N Number of consecutive successors of n having the same number of prime factors as n (counted with multiplicity).

%C If a(n) > 0 then a(n+1) = a(n)-1.

%H Antti Karttunen, <a href="/A077655/b077655.txt">Table of n, a(n) for n = 1..100000</a>

%e 33=3*11 has only two successors also with two factors: 34=2*17 and 35=5*7 (whereas 33+3=36=2*2*3*3), therefore a(33)=2.

%t snpf[n_]:=Module[{f=PrimeOmega[n],k=0},While[f==PrimeOmega[n+k],k++];k]; Array[snpf,110]-1 (* _Harvey P. Dale_, Aug 01 2021 *)

%o (PARI) A077655(n) = { my(k=n+1,w=bigomega(n)); while(bigomega(k)==w,k++); (k-n)-1; }; \\ _Antti Karttunen_, Jan 22 2020

%Y Cf. A001222, A077656, A045920, A045939, A045940, A045941, A045942, A077657.

%K nonn

%O 1,33

%A _Reinhard Zumkeller_, Nov 13 2002

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Last modified April 25 11:39 EDT 2024. Contains 371969 sequences. (Running on oeis4.)