A346247 Sum of A344587 (the deficiency of prime shifted n) and its Dirichlet inverse.

2, 0, 0, 4, 0, 16, 0, 12, 16, 24, 0, 16, 0, 40, 48, 37, 0, 28, 0, 28, 80, 48, 0, 36, 36, 64, 88, 52, 0, -48, 0, 114, 96, 72, 120, 54, 0, 88, 128, 68, 0, -64, 0, 64, 116, 112, 0, 92, 100, 68, 144, 88, 0, 124, 144, 132, 176, 120, 0, -12, 0, 144, 204, 349, 192, -72, 0, 100, 224, -72, 0, 128, 0, 160, 160, 124, 240, -88, 0, 182

Offset

1,1

Links

Antti Karttunen, Table of n, a(n) for n = 1..16383

Index entries for sequences computed from indices in prime factorization

Index entries for sequences related to sigma(n)

Formula

a(n) = A344587(n) + A346246(n).

a(n) = A323911(A003961(n)).

Prog

(PARI)
up_to = 16384;
DirInverseCorrect(v) = { my(u=vector(#v)); u[1] = (1/v[1]); for(n=2, #v, u[n] = (-u[1]*sumdiv(n, d, if(d<n, v[n/d]*u[d], 0)))); (u) }; \\ Compute the Dirichlet inverse of the sequence given in input vector v.
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)); };
v346246 = DirInverseCorrect(vector(up_to, n, A344587(n)));
A346246(n) = v346246[n];
A346247(n) = (A344587(n)+A346246(n));

Crossrefs

Cf. A000203, A003961, A323911, A344587, A346246.

Cf. also A346250.

Sequence in context: A349383 A359428 A354867 * A323412 A349354 A354352

Adjacent sequences: A346244 A346245 A346246 * A346248 A346249 A346250

Keyword

sign

Author

Antti Karttunen, Jul 19 2021

Status

approved