cp's OEIS Frontend

A336841 Prime-shifted analog of A094471: a(n) = A336845(n) - A003973(n).

%I A336841 #31 Mar 05 2021 13:55:10
%S A336841 0,2,4,14,6,36,10,68,44,52,12,192,16,84,92,284,18,326,22,274,148,100,
%T A336841 28,840,90,132,344,438,30,648,36,1094,176,148,212,1622,40,180,232,
%U A336841 1192,42,1032,46,520,802,228,52,3324,230,654,260,684,58,2376,252,1896,316,244,60,3156,66,292,1278,4010,332,1224,70,766
%N A336841 Prime-shifted analog of A094471: a(n) = A336845(n) - A003973(n).
%C A336841 All terms are even because A003973 and A336845 match parity-wise. Also in the sum formulas, only even terms are summed (only one of which is zero).
%H A336841 Antti Karttunen, <a href="/A336841/b336841.txt">Table of n, a(n) for n = 1..16384</a>
%H A336841 Antti Karttunen, <a href="/A336841/a336841.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%H A336841 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A336841 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A336841 a(n) = A336845(n) - A003973(n) = (A000005(n)*A003961(n)) - A000203(A003961(n)).
%F A336841 a(n) = A094471(A003961(n)).
%F A336841 a(n) = Sum_{d|n} (A003961(n)-A003961(d)) = Sum_{d|A003961(n)} (A003961(n)-d).
%F A336841 a(n) = 2*A336854(n) = 2*Sum_{d|n} (A048673(n)-A048673(d)).
%F A336841 a(n) = ((A003961(n)+1)*A000005(n)) - 2*A336840(n).
%F A336841 a(n) = 2 * ((A000005(n)*A048673(n)) - A336840(n)).
%F A336841 a(n) = A000005(n) * (A336837(n)/A336839(n)) = A336837(n) * A336856(n).
%o A336841 (PARI)
%o A336841 A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
%o A336841 A336841(n) = ((numdiv(n)*A003961(n)) - sigma(A003961(n)));
%o A336841 (PARI) A336841(n) = sumdiv(n,d,(A003961(n)-A003961(d)));
%o A336841 (PARI) A336841(n) = sumdiv(A003961(n),d,(A003961(n)-d));
%Y A336841 Cf. A000005, A000203, A003961, A048673, A094471, A336837, A336839, A336840, A336845, A336856.
%Y A336841 Cf. A336846 [= gcd(a(n), A003973(n))].
%Y A336841 Twice the terms of A336854.
%K A336841 nonn
%O A336841 1,2
%A A336841 _Antti Karttunen_, Aug 06 2020