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A347098 a(1) = 1; a(n) = -Sum_{d|n, d < n} A336853(n/d) * a(d), where A336853(n) = A003961(n) - n. 3
1, -1, -2, -4, -2, -5, -4, -10, -12, -7, -2, -1, -4, -11, -12, -16, -2, -1, -4, -7, -18, -13, -6, 42, -20, -17, -42, -5, -2, 21, -6, -4, -24, -19, -26, 106, -4, -23, -30, 38, -2, 45, -4, -25, -10, -29, -6, 196, -56, -17, -36, -23, -6, 123, -28, 82, -42, -31, -2, 225, -6, -37, 4, 80, -38, 15, -4, -43, -52, 39, -2, 413 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Dirichlet inverse of the pointwise sum of A336853 and A063524 (1, 0, 0, 0, ...).

LINKS

Table of n, a(n) for n=1..72.

Index entries for primes, gaps between

Index entries for sequences computed from indices in prime factorization

FORMULA

a(1) = 1; and for n > 1, a(n) = -Sum_{d|n, d < n} A336853(n/d) * a(d).

For all n >= 1, a(A000040(n)) = -A001223(n).

PROG

(PARI)

up_to = 16384;

A336853(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); (factorback(f)-n); };

Aux347098(n) = if(1==n, n, A336853(n));

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.

v347098 = DirInverseCorrect(vector(up_to, n, Aux347098(n)));

A347098(n) = v347098[n];

CROSSREFS

Cf. A000040, A001223, A003961, A336853, A347099, A347100.

Cf. also A346248, A347096.

Sequence in context: A183225 A020774 A291303 * A229920 A201562 A190041

Adjacent sequences:  A347095 A347096 A347097 * A347099 A347100 A347101

KEYWORD

sign

AUTHOR

Antti Karttunen, Aug 19 2021

STATUS

approved

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Last modified October 21 23:34 EDT 2021. Contains 348160 sequences. (Running on oeis4.)