A354824 - OEIS

A354824

Dirichlet inverse of A351084, where A351084(n) = gcd(n, A328572(n)), and A328572 converts the primorial base expansion of n into its prime product form, but with 1 subtracted from all nonzero digits.

1, -1, -1, 0, -1, 1, -1, 0, 0, 1, -1, 0, -1, 1, -3, 0, -1, 0, -1, -4, 1, 1, -1, 0, -24, 1, 0, 0, -1, 7, -1, 0, 1, 1, 1, 0, -1, 1, 1, 8, -1, -1, -1, 0, 4, 1, -1, 0, 0, 24, 1, 0, -1, 0, -3, 0, 1, 1, -1, 4, -1, 1, -6, 0, 1, -1, -1, 0, 1, -7, -1, 0, -1, 1, 52, 0, -5, -1, -1, -8, 0, 1, -1, -6, -3, 1, 1, 0, -1, -8, -5, 0

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OFFSET

1,15

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..30030

Index entries for sequences related to primorial base

FORMULA

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} A351084(n/d) * a(d).

PROG

(PARI)

A328572(n) = { my(m=1, p=2); while(n, if(n%p, m *= p^((n%p)-1)); n = n\p; p = nextprime(1+p)); (m); };

A351084(n) = gcd(n, A328572(n));

memoA354824 = Map();

A354824(n) = if(1==n, 1, my(v); if(mapisdefined(memoA354824, n, &v), v, v = -sumdiv(n, d, if(d<n, A351084(n/d)*A354824(d), 0)); mapput(memoA354824, n, v); (v)));

CROSSREFS

Cf. A351084.

Cf. also A346242, A354347, A354348, A354823.

Sequence in context: A316896 A230626 A363946 * A183700 A275478 A248678

Adjacent sequences: A354821 A354822 A354823 * A354825 A354826 A354827

KEYWORD

sign

AUTHOR

Antti Karttunen, Jun 09 2022

STATUS

approved