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A379216 Difference 2*k - A003961(k) computed for k for which this difference divides difference (A003961(k)-sigma(k)), where A003961 is fully multiplicative with a(prime(i)) = prime(i+1).

%I A379216 #10 Dec 20 2024 16:12:24
%S A379216 1,1,1,-1,-3,3,-1,1,1,-43,1,5,19,-1,-7,-5,1,-2005,1,-1,149,-193,-1,-3,
%T A379216 -79243,1243,1253,-7,51,581,-1,3093,1,155491,919,1,-1,15833,-877,
%U A379216 -4295498497,5129369,31,5779339,-69187,-29,6745,1,181,1,69197,-397,-117433,-101,-1,1,2759,1,-29479,1,-5626288431709,29669,-1,-132239,-1,-1,14591,-2267959,-3187,787250461
%N A379216 Difference 2*k - A003961(k) computed for k for which this difference divides difference (A003961(k)-sigma(k)), where A003961 is fully multiplicative with a(prime(i)) = prime(i+1).
%C A379216 Among the initial 69 terms, there are eleven +1's and eleven -1's. The former correspond in A378980 with those of its terms that are in A048674 (1, 2, 3, 25, 26, 33, 93, 1034, ...), while the latter here correspond in A378980 with those of its terms that are in A348514 (4, 10, 57, 1054, 2626, ...).
%H A379216 <a href="/index/Pri#prime_indices">Index entries for sequences related to prime indices in the factorization of n</a>.
%H A379216 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>.
%F A379216 a(n) = -A252748(A378980(n)).
%o A379216 (PARI)
%o A379216 A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
%o A379216 A378981(n) = ((A003961(n)-sigma(n))%((2*n)-A003961(n)));
%o A379216 is_A378980(n) = !A378981(n);
%o A379216 for(n=1,2^25,if(is_A378980(n),print1((2*n)-A003961(n),", ")));
%Y A379216 Cf. A003961, A048674, A252748, A348514, A378980, A378981, A379217.
%K A379216 sign
%O A379216 1,5
%A A379216 _Antti Karttunen_, Dec 20 2024