The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A354824

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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.
(history; published version)

#8 by Michael De Vlieger at Thu Jun 09 11:41:28 EDT 2022

STATUS

proposed

approved

#7 by Antti Karttunen at Thu Jun 09 10:22:14 EDT 2022

STATUS

editing

proposed

#6 by Antti Karttunen at Thu Jun 09 10:19:22 EDT 2022

LINKS

Antti Karttunen, <a href="/A354824/b354824.txt">Table of n, a(n) for n = 1..30030</a>

<a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>

STATUS

approved

editing

#5 by Michael De Vlieger at Thu Jun 09 08:45:11 EDT 2022

STATUS

proposed

approved

#4 by Antti Karttunen at Thu Jun 09 04:44:24 EDT 2022

STATUS

editing

proposed

#3 by Antti Karttunen at Thu Jun 09 04:33:43 EDT 2022

CROSSREFS

Cf. also A346242, A354347, A354348, A354823.

#2 by Antti Karttunen at Thu Jun 09 04:23:12 EDT 2022

NAME

allocated for Antti KarttunenDirichlet 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.

DATA

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

OFFSET

1,15

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.

KEYWORD

allocated

sign

AUTHOR

Antti Karttunen, Jun 09 2022

STATUS

approved

editing

#1 by Antti Karttunen at Tue Jun 07 08:26:43 EDT 2022

NAME

allocated for Antti Karttunen

KEYWORD

allocated

STATUS

approved