cp's OEIS Frontend

A378983 Numbers k such that (A003961(k)-2*k) divides (A003961(k)-(1+sigma(k))), where A003961 is fully multiplicative with a(prime(i)) = prime(i+1), and sigma is the sum of divisors function.

%I A378983 #17 Mar 31 2025 06:59:59
%S A378983 1,2,3,4,5,8,10,11,15,16,17,25,26,29,32,33,35,39,41,57,59,64,71,93,
%T A378983 101,107,125,128,137,149,161,179,191,197,227,239,256,269,281,311,347,
%U A378983 419,431,461,512,521,569,599,617,641,659,782,809,821,827,857,881,1019,1024,1030,1031,1034,1049,1054,1061,1091,1151
%N A378983 Numbers k such that (A003961(k)-2*k) divides (A003961(k)-(1+sigma(k))), where A003961 is fully multiplicative with a(prime(i)) = prime(i+1), and sigma is the sum of divisors function.
%C A378983 Conjecture: A202274 gives all terms of A028982 that occur in this sequence.
%H A378983 Antti Karttunen, <a href="/A378983/b378983.txt">Table of n, a(n) for n = 1..20000</a>
%e A378983 For k=16 we have A003961(16) = 81, A003961(k)-2*k = 49, and 49 divides (A003961(k)-(1+sigma(k))) = 81-32 = 49, therefore 16 is included in this sequence.
%e A378983 For k=25 we have A003961(25) = 49, A003961(k)-2*k = -1, and -1 divides (A003961(k)-(1+sigma(k))) regardless of what the latter is, therefore 25 is included.
%o A378983 (PARI) isA378983(n) = !A378982(n);
%Y A378983 Positions of 0's in A378982.
%Y A378983 Subsequences: A048674, A348514, A202274.
%Y A378983 Cf. also A378980.
%K A378983 nonn
%O A378983 1,2
%A A378983 _Antti Karttunen_, Dec 13 2024