A340198 - OEIS

A340198

Dirichlet inverse of sequence f(n) = A319340(n)-1 = (A000010(n) + A023900(n) - 1), where A000010 is Euler Totient function phi, and A023900 is its Dirichlet inverse.

1, 1, 1, 1, 1, -1, 1, -1, -2, -5, 1, -8, 1, -9, -13, -9, 1, -16, 1, -22, -21, -17, 1, -28, -14, -21, -20, -36, 1, -43, 1, -31, -37, -29, -45, -49, 1, -33, -45, -62, 1, -67, 1, -64, -64, -41, 1, -69, -34, -64, -61, -78, 1, -68, -77, -96, -69, -53, 1, -88, 1, -57, -96, -79, -93, -115, 1, -106, -85, -123, 1, -95, 1, -69

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OFFSET

1,9

COMMENTS

Conversely, the Dirichlet inverse of this sequence yields a sequence which is one less than A319340, i.e., pointwise sum s(n) = A109606(n) + A023900(n).

a(9796) = 0 is the only zero among the first 2^22 terms.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..16384

FORMULA

a(1) = 1, for n > 1, a(n) = -Sum_{d|n, d<n} (A319340(n/d)-1) * a(d).

PROG

(PARI)

A023900(n) = factorback(apply(p -> 1-p, factor(n)[, 1]));

A319340(n) = (eulerphi(n)+A023900(n));

A340198(n) = if(1==n, 1, -sumdiv(n, d, if(d<n, (A319340(n/d)-1)*A340198(d), 0)));

CROSSREFS

Cf. A000010, A023900, A109606, A319340, A340090, A340094, A340197, A340367.