cp's OEIS Frontend

A378736 Greatest divisor d of the n-th abundant number such that sigma(d) <= 2*d < A003961(d).

%I A378736 #18 Dec 12 2024 15:14:49
%S A378736 6,9,10,8,15,9,10,21,16,27,28,15,6,35,9,39,16,28,44,45,32,50,6,52,27,
%T A378736 28,57,15,63,44,69,35,16,75,52,32,81,28,6,44,45,6,64,98,99,50,68,52,
%U A378736 105,27,110,6,32,76,117,16,6,63,6,130,44,135,136,92,35,6,32,147,75,152,153,154,52,6,64,81,165,28,170,171
%N A378736 Greatest divisor d of the n-th abundant number such that sigma(d) <= 2*d < A003961(d).
%C A378736 There are no 1's in this sequence. See A378662, A378664 and A337372 for a proof.
%H A378736 Antti Karttunen, <a href="/A378736/b378736.txt">Table of n, a(n) for n = 1..20000</a>
%F A378736 a(n) = A378664(A005101(n)).
%F A378736 a(n) <= A378735(n).
%o A378736 (PARI)
%o A378736 A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
%o A378736 A294935(n) = (sigma(n)<=(2*n));
%o A378736 A341612(n) = ((sigma(n)<=(2*n))&&((2*n)<A003961(n)));
%o A378736 A378664(n) = { fordiv(n,d,if(A341612(n/d), return(n/d))); (1); };
%o A378736 k=0; n=0; while(k<20000, n++; if(!A294935(n), k++; print1(A378664(n),", ")));
%Y A378736 Cf. A003961, A005101, A294935, A341612, A378664, A378735, A378737.
%Y A378736 Cf. also A337372.
%K A378736 nonn
%O A378736 1,1
%A A378736 _Antti Karttunen_, Dec 06 2024
%E A378736 Unnecessary escape-clause removed from the definition by _Antti Karttunen_, Dec 12 2024