A348736 - OEIS

%I #15 Nov 15 2021 09:53:33

%S 0,1,1,-7,4,4,5,5,-20,9,6,-10,9,12,13,-33,14,-11,17,9,17,17,17,18,-9,

%T 22,5,6,28,28,14,-23,23,31,33,-283,27,36,31,37,34,38,41,-11,16,40,39,

%U -50,-36,16,45,8,47,32,50,50,53,57,30,38,48,45,5,-1027,61,56,63,35,57,68,40,-15,70,64,7,54,67,70,69,31

%N a(n) = n - A326042(n), where A326042(n) = A064989(sigma(A003961(n))).

%H Antti Karttunen, <a href="/A348736/b348736.txt">Table of n, a(n) for n = 1..20000</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

%F a(n) = n - A064989(A161942(A003961(n))).

%o (PARI)

%o A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From A003961

%o A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};

%o A326042(n) = A064989(sigma(A003961(n)));

%o A348736(n) = (n-A326042(n));

%Y Cf. A000203, A003961, A064989, A326042, A348746 [= n - A161942(n)], A348940.

%Y Cf. A348737, A348738 (positions of positive terms), A348739 (of negative terms).

%K sign

%O 1,4

%A _Antti Karttunen_, Nov 02 2021