A378231 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).

1, 5, 19, 41, 41, 47, 109, 365, 469, 141, 155, 299, 271, 449, 683, 3281, 341, 1097, 505, 1041, 1927, 663, 811, 2567, 2001, 1211, 11719, 3509, 929, -921, 1331, 29525, 2777, 1545, 4277, 6749, 1639, 2333, 4933, 9141, 1805, 851, 2161, 5235, 16733, 3815, 2755, 22979, 13177, 6805, 6239, 9671, 3421, 27347, 6131, 31049

Offset: 1

Author

Antti Karttunen, Nov 23 2024

Keywords

• sign

Comments

See comments in A377879 and in A337339.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000
• Index entries for sequences computed from indices in prime factorization.
• Index entries for sequences related to sigma(n).

Crossrefs

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

Cf. also A337339.

Programs

PARI

A003961(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); }; \\ From A003961
A344587(n) = { my(u=A003961(n)); (u+u - sigma(u)); };
A378231(n) = A344587(n^2);

Formula

a(n) = A344587(n^2) = A377879(A003961(n)).