A364574 -id:A364574 - cp's OEIS frontend

A364575 a(n) = A364574(A005940(1+n)), where A364574 is the Dirichlet inverse of A005941 [the inverse permutation of A005940].

1, -2, -3, 0, -5, 6, 2, 0, -9, 10, 19, 0, 12, -4, 0, 0, -17, 18, 35, 0, 69, -38, -22, 0, 56, -24, -64, 0, -24, 0, 0, 0, -33, 34, 67, 0, 133, -70, -42, 0, 265, -138, -339, 0, -276, 44, 8, 0, 240, -112, -288, 0, -640, 128, 124, 0, -336, 48, 176, 0, 48, 0, 0, 0, -65, 66, 131, 0, 261, -134, -82, 0, 521, -266, -659, 0

Offset: 0

Antti Karttunen, Aug 05 2023

Antti Karttunen, Table of n, a(n) for n = 0..16383

Cf. A005940, A005941, A085405 (reduced modulo 2), A364574.

Cf. also A324052, A324640 (scatter plots).

A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };
A005941(n) = { my(f=factor(n), p, p2=1, res=0); for(i=1, #f~, p = 1 << (primepi(f[i, 1])-1); res += (p * p2 * (2^(f[i, 2])-1)); p2 <<= f[i, 2]); (1+res) }; \\ (After David A. Corneth's program for A156552)
memoA364574 = Map();
A364574(n) = if(1==n,1,my(v); if(mapisdefined(memoA364574,n,&v), v, v = -sumdiv(n,d,if(dA005941(n/d)*A364574(d),0)); mapput(memoA364574,n,v); (v)));
A364575(n) = A364574(A005940(1+n));

a(n) = A364574(A005940(1+n)).

A364952 Dirichlet inverse of A364557, which is Möbius transform of A005941.

Original entry on oeis.org

1, -1, -2, -1, -4, 2, -8, -1, 0, 4, -16, 2, -32, 8, 12, -1, -64, 0, -128, 4, 24, 16, -256, 2, 8, 32, 0, 8, -512, -12, -1024, -1, 48, 64, 56, 0, -2048, 128, 96, 4, -4096, -24, -8192, 16, -8, 256, -16384, 2, 48, -8, 192, 32, -32768, 0, 112, 8, 384, 512, -65536, -12, -131072, 1024, -16, -1, 224, -48, -262144, 64, 768

Offset: 1

Antti Karttunen, Aug 29 2023

sign

Antti Karttunen, Table of n, a(n) for n = 1..10000
Index entries for sequences computed from indices in prime factorization

Cf. A000079, A000720, A005941, A364557, A364953.

Cf. also A364574.

A364557(n) = if(1==n, 1, 2^(primepi(vecmax(factor(n)[, 1]))+(bigomega(n)-omega(n))-1));
memoA364952 = Map();
A364952(n) = if(1==n,1,my(v); if(mapisdefined(memoA364952,n,&v), v, v = -sumdiv(n,d,if(dA364557(n/d)*A364952(d),0)); mapput(memoA364952,n,v); (v)));

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, dA364557(n/d) * a(d).

a(p) = -A000079(A000720(p)-1) for all primes p.

cp's OEIS Frontend

A364575 a(n) = A364574(A005940(1+n)), where A364574 is the Dirichlet inverse of A005941 [the inverse permutation of A005940].

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