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a(n) = (A337339(n)-A003961(n)) / 2.
3

%I #9 Aug 24 2020 22:29:56

%S 0,1,4,16,9,49,25,169,144,100,36,484,64,38,289,1600,81,1369,121,961,

%T 729,361,196,4489,576,625,3844,139,225,2704,324,14641,1024,784,1444,

%U 12544,400,1156,1764,8836,441,6724,529,3364,7569,1849,676,40804,3600,5329,2209,5776,841,34969,2025,4262,3249,386,900,24649,1089

%N a(n) = (A337339(n)-A003961(n)) / 2.

%C Not all terms are squares. For example, a(14) = 38, a(28) = 139 and a(56) = 4262 are not squares.

%C Not all terms are nonnegative. The first three negative terms are a(1354) = -290, a(7078) = -1363 and a(15722) = -2386.

%H Antti Karttunen, <a href="/A337340/b337340.txt">Table of n, a(n) for n = 1..8191</a>

%H Antti Karttunen, <a href="/A337340/a337340.txt">Data supplement: n, a(n) computed for n = 1..65537</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>

%o (PARI)

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

%o A337340(n) = { my(h=A003961(n),s=(h^2),u=(s+1)/2); ((u/gcd(1+sigma(s), u)) - h)/2; };

%Y Cf. A003961, A337337, A337339.

%Y Cf. also A337341.

%K sign

%O 1,3

%A _Antti Karttunen_, Aug 24 2020