cp's OEIS Frontend

A366387 Divide n by its smallest prime factor, then multiply with the index of that same prime; a(1) = 0 by convention.

%I A366387 #14 Oct 23 2023 15:15:01
%S A366387 0,1,2,2,3,3,4,4,6,5,5,6,6,7,10,8,7,9,8,10,14,11,9,12,15,13,18,14,10,
%T A366387 15,11,16,22,17,21,18,12,19,26,20,13,21,14,22,30,23,15,24,28,25,34,26,
%U A366387 16,27,33,28,38,29,17,30,18,31,42,32,39,33,19,34,46,35,20,36,21,37,50,38,44,39,22,40,54,41,23,42,51
%N A366387 Divide n by its smallest prime factor, then multiply with the index of that same prime; a(1) = 0 by convention.
%H A366387 Antti Karttunen, <a href="/A366387/b366387.txt">Table of n, a(n) for n = 1..16384</a>
%H A366387 <a href="/index/Mat#matula">Index entries for sequences related to Matula-Goebel numbers</a>
%H A366387 <a href="/index/Pri#prime_indices">Index entries for sequences related to prime indices in the factorization of n</a>
%F A366387 a(n) = A032742(n) * A055396(n) = (n/A020639(n)) * A000720(A020639(n)).
%F A366387 a(2n) = n, a(3*(2n+1)) = 2*(2n+1) = 4n + 2.
%t A366387 Array[PrimePi[#2]*#1/#2 & @@ {#, FactorInteger[#][[1, 1]]} &, 85] (* _Michael De Vlieger_, Oct 23 2023 *)
%o A366387 (PARI)
%o A366387 A020639(n) = if(1==n,n,vecmin(factor(n)[, 1]));
%o A366387 A366387(n) = { my(spf=A020639(n)); primepi(spf)*(n/spf); };
%Y A366387 Cf. A000720, A020639, A032742, A055396.
%Y A366387 Cf. A196050 (number of iterations needed to reach 1), A324923.
%Y A366387 Cf. also A366385, and A060681 (divide by the smallest prime p, then multiply with p-1),
%K A366387 nonn
%O A366387 1,3
%A A366387 _Antti Karttunen_, Oct 23 2023