A324336 -id:A324336 - cp's OEIS frontend

A324335 a(n) = A323363(A005940(1+n)), where A005940 is the Doudna sequence and A323363 is the Dirichlet inverse of Dedekind's psi.

1, -3, -4, 3, -6, 12, 4, -3, -8, 18, 24, -12, 6, -12, -4, 3, -12, 24, 32, -18, 48, -72, -24, 12, 8, -18, -24, 12, -6, 12, 4, -3, -14, 36, 48, -24, 72, -96, -32, 18, 96, -144, -192, 72, -48, 72, 24, -12, 12, -24, -32, 18, -48, 72, 24, -12, -8, 18, 24, -12, 6, -12, -4, 3, -18, 42, 56, -36, 84, -144, -48, 24, 112, -216, -288, 96, -72, 96, 32, -18

Offset: 0

Antti Karttunen, Feb 23 2019

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Antti Karttunen, Table of n, a(n) for n = 0..16383
Antti Karttunen, Data supplement: n, a(n) computed for n = 0..65537
Index entries for sequences related to binary expansion of n

Cf. A001615, A005940, A323363, A323915, A324336.

A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t }; \\ From A005940
A001615(n) = (n * sumdivmult(n, d, issquarefree(d)/d)); \\ From A001615
memoA323363 = Map();
A323363(n) = if(1==n,1,my(v); if(mapisdefined(memoA323363,n,&v), v, v = -sumdiv(n,d,if(dA001615(n/d)*A323363(d),0)); mapput(memoA323363,n,v); (v)));
A324335(n) = A323363(A005940(1+n));

a(n) = A323363(A005940(1+n)).

A324340 a(n) = A046692(A005940(1+n)), where A005940 is the Doudna sequence and A046692 is the Dirichlet inverse of sigma function.

Original entry on oeis.org

1, -3, -4, 2, -6, 12, 3, 0, -8, 18, 24, -8, 5, -9, 0, 0, -12, 24, 32, -12, 48, -72, -18, 0, 7, -15, -20, 6, 0, 0, 0, 0, -14, 36, 48, -16, 72, -96, -24, 0, 96, -144, -192, 48, -40, 54, 0, 0, 11, -21, -28, 10, -42, 60, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0, -18, 42, 56, -24, 84, -144, -36, 0, 112, -216, -288, 64, -60, 72, 0, 0, 168, -288, -384, 96, -576, 576, 144, 0

Offset: 0

Antti Karttunen, Feb 24 2019

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Antti Karttunen, Table of n, a(n) for n = 0..16383
Antti Karttunen, Data supplement: n, a(n) computed for n = 0..65537
Index entries for sequences related to binary expansion of n

Cf. A005940, A046692.

Cf. also A323915, A324335, A324336, A324339.

A324340(n) = { my(m1=1, p=2); while(n, if(!(n%2), p=nextprime(1+p); n>>=1, if(1==(n%4), m1 *= -(1+p), if(3==(n%8), m1 *= p, return(0))); while((n%2),n>>=1))); (m1); };

A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t }; \\ From A005940
A046692(n) = { my(f=factor(n)~); prod(i=1, #f, if(1==f[2,i], -(f[1,i]+1), if(2==f[2,i], f[1,i], 0))); };
A324340(n) = A046692(A005940(1+n));

a(n) = A046692(A005940(1+n)).

A324339 a(n) = A246707(A005940(1+n)), where A005940 is the Doudna sequence, and A246707 is the expansion of phi(-q) * phi(-q^2) * phi(-q^3) * phi(-q^6) in powers of q.

Original entry on oeis.org

-2, -2, 2, 6, 4, -14, -2, 6, 0, -12, -4, 42, 2, -50, 2, 6, -8, -16, 0, 36, 0, -84, 4, 42, 14, -62, -2, 150, -24, -158, -2, 6, 4, -24, 8, 48, 16, -112, 0, 36, 0, -96, 0, 252, 0, -300, -4, 42, -10, -114, -14, 186, -28, -434, 2, 150, 0, -312, 24, 474, 38, -482, 2, 6, -4, -28, -4, 72, -8, -168, -8, 48, 0, -144, -16, 336, 8, -400, 0, 36, 16

Offset: 0

Antti Karttunen, Feb 23 2019

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Antti Karttunen, Table of n, a(n) for n = 0..1505
Index entries for sequences related to binary expansion of n

Cf. A005940, A246707.

Cf. also A323915, A324335, A324336, A324340.

A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t }; \\ From A005940
A246707(n) = { local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x + A)^2 * eta(x^2 + A) * eta(x^3 + A)^2 * eta(x^6 + A) / (eta(x^4 + A) * eta(x^12 + A)), n)); }; \\ From A246707
A324339(n) = A246707(A005940(1+n));

a(n) = A246707(A005940(1+n)).

cp's OEIS Frontend

A324335 a(n) = A323363(A005940(1+n)), where A005940 is the Doudna sequence and A323363 is the Dirichlet inverse of Dedekind's psi.

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A324340 a(n) = A046692(A005940(1+n)), where A005940 is the Doudna sequence and A046692 is the Dirichlet inverse of sigma function.

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PARI

PARI

Formula

A324339 a(n) = A246707(A005940(1+n)), where A005940 is the Doudna sequence, and A246707 is the expansion of phi(-q) * phi(-q^2) * phi(-q^3) * phi(-q^6) in powers of q.

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