A378231 - OEIS

%I #10 Nov 23 2024 19:37:34

%S 1,5,19,41,41,47,109,365,469,141,155,299,271,449,683,3281,341,1097,

%T 505,1041,1927,663,811,2567,2001,1211,11719,3509,929,-921,1331,29525,

%U 2777,1545,4277,6749,1639,2333,4933,9141,1805,851,2161,5235,16733,3815,2755,22979,13177,6805,6239,9671,3421,27347,6131,31049

%N Deficiency of prime-shifted squares: a(n) = 2*A003961(n^2) - sigma(A003961(n^2)), where A003961 is fully multiplicative function with a(prime(i)) = prime(i+1).

%C See comments in A377879 and in A337339.

%H Antti Karttunen, <a href="/A378231/b378231.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) = A344587(n^2) = A377879(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 A344587(n) = { my(u=A003961(n)); (u+u - sigma(u)); };

%o A378231(n) = A344587(n^2);

%Y Cf. A000203, A003961, A003973, A033879, A344587, A377879.

%Y Cf. also A337339.

%K sign

%O 1,2

%A _Antti Karttunen_, Nov 23 2024