cp's OEIS Frontend

A347390 Odd numbers k that can be factored to such a pair of coprime factors x and y that A347381(k) < min(A347381(x), A347381(y)).

%I A347390 #15 Sep 17 2021 16:16:12
%S A347390 189,455,945,1271,1365,2125,4199,6375,9261,12597,13167,15631,18189,
%T A347390 20995,21275,24583,26273,29393,30879,42813,43475,46163,46189,46305,
%U A347390 46575,46893,54653,63767,63825,65317,67473,67673,73749,78155,78725,89503,90117,90945,92783,93869,106079,108819,119239,122265,127323,129575
%N A347390 Odd numbers k that can be factored to such a pair of coprime factors x and y that A347381(k) < min(A347381(x), A347381(y)).
%H A347390 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A347390 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%e A347390 189 is a term, because A347381(189) = 1, and 189 can be factored as 7*27 with gcd(7,27)=1, and A347381(7) = A347381(27) = 3 > 1.
%e A347390 455 is a term, because A347381(455) = 2, and 455 can be factored as 7*65 with gcd(7,65)=1, and A347381(65) = 4 > A347381(7) = 3 > A347381(455) = 2.
%e A347390 945 is a term, because A347381(945) = 1, and 945 can be factored as 27*35 with gcd(27,35)=1, and A347381(27) = 3 > A347381(35) = 2 > A347381(945) = 1.
%e A347390 1542968918569 = (13*19*47*107)^2 is a term, because it can be factored as 893^2 * 1391^2, with gcd(893^2, 1391^2) = 1, and A347381(1391^2) = 30 > A347381(893^2) = 17 > A347381(1542968918569) = 12. (This is probably the smallest square present in the sequence).
%o A347390 (PARI) isA347390(n) = if(!(n%2),0,my(w=A347381(n)); fordiv(n,d,if(d>(n/d),return(0)); if(1==gcd(d,n/d) && (min(A347381(d),A347381(n/d))>w), return(1))); (0));
%Y A347390 Cf. A347381, A347391.
%Y A347390 Subsequence of A347384. Cf. also A347383 (subsequence).
%K A347390 nonn
%O A347390 1,1
%A A347390 _Antti Karttunen_, Sep 09 2021