A349400 -id:A349400

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A349614

Dirichlet convolution of A064664 (the inverse permutation of EKG-permutation, A064413) with the Dirichlet inverse of A064413.

+10
9

1, 0, 1, -3, 7, -7, 2, 6, -8, -10, 5, 9, 14, 2, -41, -1, 17, 27, 15, -6, -38, -18, 13, 10, -32, -29, 18, 33, 18, 62, 29, -13, -31, -53, -107, 25, 48, -51, -86, 13, 30, 116, 58, 23, 88, -34, 37, -47, -30, 56, -113, 3, 45, -39, -137, -154, -73, -67, 41, 160, 84, -91, 174, 56, -154, 152, 91, 6, -113, 246, 58, -185, 56

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OFFSET

1,4

COMMENTS

Obviously, convolving this with A064413 gives its inverse permutation A064664.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..20000

Index entries for sequences related to EKG sequence

FORMULA

a(n) = Sum_{d|n} A064664(d) * A349400(n/d).

PROG

(PARI)

up_to = 32768;

v064413 = readvec("b064413_upto65539_terms_only.txt"); \\ Data prepared with Chai Wah Wu's Dec 08 2014 Python-program given in A064413.

A064413(n) = v064413[n];

\\ Then its inverse A064664 is prepared:

m064664 = Map();

for(n=1, 65539, mapput(m064664, A064413(n), n));

A064664(n) = mapget(m064664, n);

memoA349400 = Map();

A349400(n) = if(1==n, 1, my(v); if(mapisdefined(memoA349400, n, &v), v, v = -sumdiv(n, d, if(d<n, A064413(n/d)*A349400(d), 0)); mapput(memoA349400, n, v); (v)));

A349614(n) = sumdiv(n, d, A064664(d)*A349400(n/d));

CROSSREFS

Cf. A064413, A064664, A349400, A349613 (Dirichlet inverse), A349615 (sum with it), A349617.

Cf. also pairs A349376, A349377 and A349397, A349398 for similar constructions.

KEYWORD

sign

AUTHOR

Antti Karttunen, Nov 23 2021

STATUS

approved

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