A347121 - OEIS

%I #13 Oct 16 2021 15:21:22

%S -1,1,2,11,2,28,4,49,31,40,2,128,4,62,66,179,2,209,4,188,102,76,6,472,

%T 59,98,218,286,2,420,6,601,126,112,146,859,4,134,162,700,2,636,4,368,

%U 498,168,6,1592,149,445,186,466,6,1252,178,1058,222,184,2,1704,6,216,756,1931,230,828,4,548,278,940,2,3041,6

%N a(n) = A347136(n) - 2*n.

%H Antti Karttunen, <a href="/A347121/b347121.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Pri#gaps">Index entries for primes, gaps between</a>

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

%F a(n) = A347136(n) - 2*n.

%F a(A000040(n)) = A001223(n).

%o (PARI)

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

%o A347121(n) = (sumdiv(n,d,d*A003961(n/d))-(2*n));

%Y Cf. A000040, A001223, A003961, A347136, A347122 (Möbius transform).

%Y Cf. also A341512, A346239, A347236.

%K sign

%O 1,3

%A _Antti Karttunen_, Aug 24 2021