A305800 -id:A305800 - cp's OEIS frontend

A353560 Lexicographically earliest infinite sequence such that a(i) = a(j) => A046523(i) = A046523(j), A001065(i) = A001065(j) and A051953(i) = A051953(j), for all i, j >= 1.

1, 2, 2, 3, 2, 4, 2, 5, 6, 7, 2, 8, 2, 9, 10, 11, 2, 12, 2, 13, 14, 15, 2, 16, 17, 18, 19, 20, 2, 21, 2, 22, 23, 24, 25, 26, 2, 27, 28, 29, 2, 30, 2, 31, 32, 33, 2, 34, 35, 36, 37, 38, 2, 39, 28, 40, 41, 42, 2, 43, 2, 44, 45, 46, 47, 48, 2, 49, 50, 51, 2, 52, 2, 53, 54, 55, 47, 56, 2, 57, 58, 59, 2, 60, 41, 61, 62, 63, 2, 64, 37

Offset: 1

Antti Karttunen, Apr 29 2022

nonn

Restricted growth sequence transform of the triplet [A046523(n), A001065(n), A051953(n)].
For all i,j:
  A305800(i) = A305800(j) => a(i) = a(j),
  a(i) = a(j) => A300232(i) = A300232(j), [Combining A046523 and A051953]
  a(i) = a(j) => A300235(i) = A300235(j), [Combining A046523 and A001065]
  a(i) = a(j) => A305895(i) = A305895(j), [Combining A001065 and A051953]
  a(i) = a(j) => A353276(i) = A353276(j). [Needs all three components]

Antti Karttunen, Table of n, a(n) for n = 1..100000

Cf. A001065, A046523, A051953.
Cf. also A101296, A305800, A300232, A353276.
Differs from A300235 for the first time at n=153, where a(153) = 110, while A300235(153) = 106.
Differs from A305895 for the first time at n=3283, where a(3283) = 2502, while A305895(3283) = 1845.
Differs from A327931 for the first time at n=4433, where a(4433) = 2950, while A327931(4433) = 3393.
Differs from A300249 and from A351260 for the first time at n=105, where a(105) = 75, while A300249(105) = A351260(105) = 56.

up_to = 100000;
rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om,invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om,invec[i],i); outvec[i] = u; u++ )); outvec; };
A001065(n) = (sigma(n)-n);
A051953(n) = (n-eulerphi(n));
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
Aux353560(n) = [A046523(n), A001065(n), A051953(n)];
v353560 = rgs_transform(vector(up_to,n,Aux353560(n)));
A353560(n) = v353560[n];

A353565 Lexicographically earliest infinite sequence such that a(i) = a(j) => A353564(i) = A353564(j), where A353564(n) = Product_{d|n, dA276086(phi(d)).

Original entry on oeis.org

1, 2, 2, 3, 2, 4, 2, 4, 5, 6, 2, 7, 2, 8, 9, 7, 2, 10, 2, 11, 12, 10, 2, 13, 14, 15, 12, 16, 2, 17, 2, 18, 19, 20, 21, 22, 2, 23, 24, 25, 2, 26, 2, 22, 27, 28, 2, 29, 30, 31, 32, 33, 2, 34, 35, 36, 37, 26, 2, 38, 2, 39, 40, 41, 42, 43, 2, 44, 45, 46, 2, 47, 2, 48, 49, 50, 42, 51, 2, 52, 40, 53, 2, 54, 27, 55, 56, 47, 2, 57

Offset: 1

Antti Karttunen, Apr 27 2022

Restricted growth sequence transform of A353564.

For all i, j: A305800(i) = A305800(j) => a(i) = a(j) => A051953(i) = A051953(j).

Antti Karttunen, Table of n, a(n) for n = 1..65537

Cf. A000010, A051953, A276086, A353563, A353564.

Cf. also A305800, A318835.

up_to = 65537;
rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om,invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om,invec[i],i); outvec[i] = u; u++ )); outvec; };
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A353564(n) = { my(m=1); fordiv(n,d,if(d < n,m *= A276086(eulerphi(d)))); m; };
v353565 = rgs_transform(vector(up_to,n,A353564(n)));
A353565(n) = v353565[n];

A366297 Lexicographically earliest infinite sequence such that a(i) = a(j) => A359589(i) = A359589(j) for all i, j >= 1, where A359589 is Dirichlet inverse of function f(n) = (-1 + gcd(A003415(n), A276086(n))).

Original entry on oeis.org

1, 2, 2, 2, 2, 3, 2, 4, 5, 2, 2, 2, 2, 4, 6, 2, 2, 2, 2, 4, 7, 2, 2, 2, 7, 8, 4, 2, 2, 2, 2, 2, 9, 2, 5, 10, 2, 11, 6, 2, 2, 2, 2, 4, 4, 12, 2, 13, 9, 8, 7, 14, 2, 15, 6, 2, 6, 2, 2, 2, 2, 4, 4, 16, 17, 2, 2, 4, 6, 2, 2, 18, 2, 4, 3, 3, 17, 2, 2, 2, 18, 2, 2, 19, 6, 8, 6, 20, 2, 21, 6, 4, 6, 22, 5, 2, 2, 14, 8, 20, 2, 14, 2, 2, 2

Offset: 1

Antti Karttunen, Oct 07 2023

nonn

Restricted growth sequence transform of A359589.

For all i, j: A305800(i) = A305800(j) => a(i) = a(j) => A359595(i) = A359595(j).

Antti Karttunen, Table of n, a(n) for n = 1..65537

Cf. A276086, A305800, A327858, A359589, A359595.

Cf. also A366296.

up_to = 65537;
rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om,invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om,invec[i],i); outvec[i] = u; u++ )); outvec; };
DirInverseCorrect(v) = { my(u=vector(#v)); u[1] = (1/v[1]); for(n=2, #v, u[n] = (-u[1]*sumdiv(n, d, if(dA003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A327858(n) = gcd(A003415(n), A276086(n));
v366297 = rgs_transform(DirInverseCorrect(vector(up_to,n,A327858(n)-1)));
A366297(n) = v366297[n];

A373379 Lexicographically earliest infinite sequence such that a(i) = a(j) => A003415(i) = A003415(j), A085731(i) = A085731(j) and A107463(i) = A107463(j), for all i, j >= 1.

Original entry on oeis.org

1, 2, 2, 3, 2, 4, 2, 5, 6, 7, 2, 8, 2, 9, 10, 11, 2, 12, 2, 13, 14, 15, 2, 16, 17, 18, 19, 20, 2, 21, 2, 22, 23, 24, 25, 26, 2, 27, 28, 29, 2, 30, 2, 31, 32, 33, 2, 34, 35, 36, 37, 38, 2, 39, 28, 40, 41, 42, 2, 43, 2, 44, 45, 46, 47, 48, 2, 49, 50, 51, 2, 52, 2, 53, 54, 55, 47, 56, 2, 57, 58, 59, 2, 60, 41, 61, 62, 63, 2, 64, 37, 65, 66, 67, 68, 69, 2, 70, 71, 72

Offset: 1

Antti Karttunen, Jun 03 2024

nonn

Restricted growth sequence transform of the triple [A003415(n), A085731(n), A107463(n)].
For all i, j >= 1:
  A305800(i) = A305800(j) => a(i) = a(j),
  a(i) = a(j) => A369051(i) = A369051(j),
  a(i) = a(j) => A373363(i) = A373363(j),
  a(i) = a(j) => A373364(i) = A373364(j).
Starts to differ from A300235 at n=153. - R. J. Mathar, Jun 06 2024

Antti Karttunen, Table of n, a(n) for n = 1..100000

Cf. A001414, A003415, A085731, A107463, A305800, A369051, A373363, A373364.
Differs from A305895, A327931, and A353560 for the first time at n=1610, where a(1610) = 1112, while A305895(1610) = A327931(1610) = A353560(1610) = 1210.
Cf. also A373150, A373152, A373380.

up_to = 100000;
rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om,invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om,invec[i],i); outvec[i] = u; u++ )); outvec; };
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A085731(n) = gcd(A003415(n),n);
A001414(n) = ((n=factor(n))[, 1]~*n[, 2]);
A107463(n) = if(n<=1,n,if(isprime(n),1,A001414(n)));
Aux373379(n) = [A003415(n), A085731(n), A107463(n)];
v373379 = rgs_transform(vector(up_to, n, Aux373379(n)));
A373379(n) = v373379[n];

A373983 Lexicographically earliest infinite sequence such that a(i) = a(j) = A246277(A324886(i)) = A246277(A324886(j)) and A278226(A328768(i)) = A278226(A328768(j)), for all i, j >= 1.

Original entry on oeis.org

1, 2, 2, 3, 2, 4, 2, 5, 5, 6, 2, 7, 2, 8, 9, 10, 2, 11, 2, 12, 13, 14, 2, 15, 16, 6, 17, 18, 2, 19, 2, 20, 21, 22, 23, 24, 2, 25, 26, 27, 2, 28, 2, 29, 30, 31, 2, 32, 33, 34, 13, 35, 2, 36, 37, 38, 39, 40, 2, 41, 2, 8, 42, 43, 44, 45, 2, 29, 46, 47, 2, 48, 2, 49, 50, 51, 52, 53, 2, 54, 55, 56, 2, 57, 58, 14, 59, 60, 2, 61, 62, 63, 13, 64, 65, 66, 2, 67, 68, 69

Offset: 1

Antti Karttunen, Jun 25 2024

Restricted growth sequence transform of the ordered pair [A246277(A276086(A108951(n))), A046523(A276086(A328768(n)))].
For all i, j >= 1:
  A305800(i) = A305800(j) => a(i) = a(j),
  a(i) = a(j) => A329345(i) = A329345(j) => A329045(i) = A329045(j),
  a(i) = a(j) => A373982(i) = A373982(j) => A328771(i) = A328771(j).
It is hard to say for sure which graphical features in the scatter plot have their provenance in A373982, and which ones in A329345.

Antti Karttunen, Table of n, a(n) for n = 1..100000
Index entries for sequences related to primorial numbers

Cf. A002110, A046523, A108951, A246277, A276086, A278226, A324886, A328768.
Cf. A305800, A329045, A329345, A328771, A373982.
Cf. also A329620.

up_to = 100000;
rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om,invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om,invec[i],i); outvec[i] = u; u++ )); outvec; };
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };
A108951(n) = { my(f=factor(n)); prod(i=1, #f~,  prod(i=1, primepi(f[i, 1]), prime(i))^f[i, 2]); };
A246277(n) = if(1==n, 0, my(f = factor(n), k = primepi(f[1,1])-1); for (i=1, #f~, f[i,1] = prime(primepi(f[i,1])-k)); factorback(f)/2);
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A002110(n) = prod(i=1,n,prime(i));
A328768(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]*A002110(primepi(f[i,1])-1)/f[i, 1]));
Aux373983(n) = [A246277(A276086(A108951(n))), A046523(A276086(A328768(n)))];
v373983 = rgs_transform(vector(up_to, n, Aux373983(n)));
A373983(n) = v373983[n];

A327162 Lexicographically earliest sequence such that for all i, j, a(i) = a(j) => f(i) = f(j), where f(n) = A034460(n) * (-1)^[A327159(n)>0], and A034460(n) = usigma(n)-n, with usigma the sum of unitary divisors of n (A034448).

Original entry on oeis.org

1, 2, 2, 2, 2, 3, 2, 2, 2, 4, 2, 4, 2, 5, 6, 2, 2, 7, 2, 5, 8, 9, 2, 7, 2, 10, 2, 7, 2, 11, 2, 2, 12, 13, 14, 9, 2, 15, 16, 9, 2, 17, 2, 10, 12, 18, 2, 13, 2, 19, 20, 21, 2, 22, 16, 10, 23, 24, 2, 25, 2, 26, 16, 2, 27, 28, 2, 15, 29, 30, 2, 21, 2, 31, 32, 33, 27, 34, 2, 15, 2, 35, 2, 36, 23, 37, 38, 13, 2, 39, 20, 19, 40, 41, 42, 43, 2, 44, 20, 45, 2, 46, 2, 15

Offset: 1

Antti Karttunen, Aug 28 2019

nonn

For all i, j:

A305800(i) = A305800(j) => a(i) = a(j) => A318882(i) = A318882(j).

Antti Karttunen, Table of n, a(n) for n = 1..87360

Cf. A034448, A034460, A305800, A318882, A327159,

up_to = 87360;
rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om,invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om,invec[i],i); outvec[i] = u; u++ )); outvec; };
A034460(n) = (sumdivmult(n, d, if(gcd(d, n/d)==1, d))-n); \\ From A034460
A327159(n,orgn=n,xs=Set([])) = if(1==n,0,if(vecsearch(xs,n), if(n==orgn,length(xs),0), xs = setunion([n],xs); A327159(A034460(n),orgn,xs)));
Aux327162(n) = A034460(n)*((-1)^((A327159(n)>0)));
v327162 = rgs_transform(vector(up_to, n, Aux327162(n)));
A327162(n) = v327162[n];

A327163 Lexicographically earliest sequence such that for all i, j, a(i) = a(j) => f(i) = f(j), where f(n) = gcd(n,usigma(n)) * (-1)^[gcd(n,usigma(n))==n], and usigma is the sum of unitary divisors of n (A034448).

Original entry on oeis.org

1, 2, 2, 2, 2, 3, 2, 2, 2, 4, 2, 5, 2, 4, 6, 2, 2, 7, 2, 8, 2, 4, 2, 9, 2, 4, 2, 5, 2, 7, 2, 2, 6, 4, 2, 4, 2, 4, 2, 4, 2, 7, 2, 5, 10, 4, 2, 5, 2, 4, 6, 4, 2, 7, 2, 11, 2, 4, 2, 12, 2, 4, 2, 2, 2, 7, 2, 4, 6, 4, 2, 13, 2, 4, 2, 5, 2, 7, 2, 4, 2, 4, 2, 5, 2, 4, 6, 5, 2, 14, 15, 5, 2, 4, 16, 9, 2, 4, 6, 8, 2, 7, 2, 4, 6

Offset: 1

Antti Karttunen, Aug 28 2019

nonn

Restricted growth sequence transform of function f, defined as f(n) = -A323166(n) = -n when n is one of unitary multiply-perfect numbers (A327158), otherwise f(n) = A323166(n) = gcd(n,A034448(n))
For all i, j:
  A305800(i) = A305800(j) => a(i) = a(j) => A327164(i) = A327164(j).

Antti Karttunen, Table of n, a(n) for n = 1..87360

Cf. A034448, A305800, A323166, A327158, A327164.

Cf. also A326193.

up_to = 87360;
rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om,invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om,invec[i],i); outvec[i] = u; u++ )); outvec; };
A034448(n) = { my(f=factorint(n)); prod(k=1, #f~, 1+(f[k, 1]^f[k, 2])); }; \\ After code in A034448
A323166(n) = gcd(n, A034448(n));
Aux327163(n) = { my(u=A323166(n)); u*((-1)^(u==n)); };
v327163 = rgs_transform(vector(up_to, n, Aux327163(n)));
A327163(n) = v327163[n];

A328767 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where for n>1, f(n) = [A003415(i), A328382(i)], and f(1) = 1.

Original entry on oeis.org

1, 2, 2, 3, 2, 4, 2, 5, 6, 7, 2, 8, 2, 9, 10, 11, 2, 12, 2, 13, 14, 15, 2, 16, 14, 17, 18, 19, 2, 20, 2, 21, 22, 23, 24, 25, 2, 26, 27, 28, 2, 29, 2, 30, 31, 32, 2, 33, 22, 34, 35, 36, 2, 37, 38, 39, 40, 41, 2, 42, 2, 43, 44, 45, 46, 47, 2, 48, 49, 50, 2, 51, 2, 52, 53, 54, 46, 55, 2, 56, 57, 58, 2, 59, 60, 61, 62, 63, 2, 64, 65, 66, 67, 68, 69, 70, 2, 71, 72, 73, 2, 74, 2

Offset: 1

Antti Karttunen, Oct 28 2019

nonn

For all i, j:
  A305800(i) = A305800(j) => a(i) = a(j),
  a(i) = a(j) => A327858(i) = A327858(j),
  a(i) = a(j) => A328098(i) = A328098(j),

Antti Karttunen, Table of n, a(n) for n = 1..65537

Cf. A003415, A305800, A327858, A328098, A328382.

Cf. also A300245, A300249, A327970.

up_to = 65537;
rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om,invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om,invec[i],i); outvec[i] = u; u++ )); outvec; };
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A328382(n) = (A276086(n)%A003415(n));
Aux328767(n) = if(1==n,1,[A003415(n), A328382(n)]);
v328767 = rgs_transform(vector(up_to, n, Aux328767(n)));
A328767(n) = v328767[n];

A373380 Lexicographically earliest infinite sequence such that a(i) = a(j) => A373145(i) = A373145(j), A373362(i) = A373362(j), and A373364(i) = A373364(j), for all i, j >= 1.

Original entry on oeis.org

1, 2, 2, 3, 2, 4, 2, 5, 6, 7, 2, 8, 2, 9, 10, 11, 2, 2, 2, 12, 13, 14, 2, 2, 13, 15, 16, 17, 2, 2, 2, 18, 19, 20, 21, 22, 2, 23, 24, 2, 2, 25, 2, 26, 2, 27, 2, 28, 19, 29, 30, 31, 2, 2, 24, 2, 32, 33, 2, 3, 2, 34, 35, 36, 37, 2, 2, 12, 38, 2, 2, 39, 2, 40, 2, 41, 37, 42, 2, 28, 43, 44, 2, 45, 32, 46, 47, 2, 2, 2, 48, 26, 49, 50, 51, 2, 2, 2, 2, 52

Offset: 1

Antti Karttunen, Jun 03 2024

nonn

Restricted growth sequence transform of the triple [A373145(n), A373362(n), A373364(n)], i.e., the triple [gcd(x, y), gcd(x, z), gcd(y, z)], where x=A001414(n), y=A003415(n), z=A276085(n).
For all i, j >= 1:
  A305800(i) = A305800(j) => a(i) = a(j),
  a(i) = a(j) => A373367(i) = A373367(j).

Antti Karttunen, Table of n, a(n) for n = 1..100000

Cf. A001414, A003415, A276085, A305800, A373145, A373362, A373364, A373367.

Cf. also A373150, A373379.

up_to = 100000;
rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om,invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om,invec[i],i); outvec[i] = u; u++ )); outvec; };
A001414(n) = ((n=factor(n))[, 1]~*n[, 2]);
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A276085(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*prod(i=1,primepi(f[k, 1]-1),prime(i))); };
Aux373380(n) = { my(x=A001414(n), y=A003415(n), z=A276085(n)); [gcd(x, y), gcd(x, z), gcd(y, z)]; };
v373380 = rgs_transform(vector(up_to, n, Aux373380(n)));
A373380(n) = v373380[n];

A373988 Lexicographically earliest infinite sequence such that a(i) = a(j) => A373986(i) = A373986(j), for all i, j >= 1.

Original entry on oeis.org

1, 2, 2, 2, 2, 3, 2, 4, 2, 5, 2, 6, 2, 7, 2, 2, 2, 8, 2, 9, 10, 11, 2, 2, 2, 12, 2, 13, 2, 14, 2, 6, 15, 16, 17, 2, 2, 18, 19, 4, 2, 20, 2, 21, 8, 22, 2, 8, 2, 23, 24, 25, 2, 6, 26, 27, 28, 29, 2, 2, 2, 30, 31, 4, 32, 33, 2, 34, 35, 36, 2, 2, 2, 37, 38, 39, 3, 40, 2, 14, 2, 41, 2, 38, 42, 43, 44, 15, 2, 38, 45, 46, 47, 48, 49, 2, 2, 50, 51, 17, 2, 52, 2, 19

Offset: 1

Antti Karttunen, Jun 25 2024

nonn

Restricted growth sequence transform of A373986.

For all i, j >= 1: A305800(i) = A305800(j) => a(i) = a(j).

Antti Karttunen, Table of n, a(n) for n = 1..100000
Index entries for sequences related to primorial numbers

Cf. A108951, A373158, A373986.

up_to = 100000;
rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om,invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om,invec[i],i); outvec[i] = u; u++ )); outvec; };
A373986(n) = { my(f=factor(n),m=1,s=0); for(i=1, #f~, my(x=prod(i=1,primepi(f[i, 1]),prime(i))); s += f[i, 2]*x; m *= x^f[i, 2]); s/gcd(m,s); };
v373988 = rgs_transform(vector(up_to, n, A373986(n)));
A373988(n) = v373988[n];

cp's OEIS Frontend

A353560 Lexicographically earliest infinite sequence such that a(i) = a(j) => A046523(i) = A046523(j), A001065(i) = A001065(j) and A051953(i) = A051953(j), for all i, j >= 1.

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A353565 Lexicographically earliest infinite sequence such that a(i) = a(j) => A353564(i) = A353564(j), where A353564(n) = Product_{d|n, dA276086(phi(d)).

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A366297 Lexicographically earliest infinite sequence such that a(i) = a(j) => A359589(i) = A359589(j) for all i, j >= 1, where A359589 is Dirichlet inverse of function f(n) = (-1 + gcd(A003415(n), A276086(n))).

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A373379 Lexicographically earliest infinite sequence such that a(i) = a(j) => A003415(i) = A003415(j), A085731(i) = A085731(j) and A107463(i) = A107463(j), for all i, j >= 1.

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A373983 Lexicographically earliest infinite sequence such that a(i) = a(j) = A246277(A324886(i)) = A246277(A324886(j)) and A278226(A328768(i)) = A278226(A328768(j)), for all i, j >= 1.

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A327162 Lexicographically earliest sequence such that for all i, j, a(i) = a(j) => f(i) = f(j), where f(n) = A034460(n) * (-1)^[A327159(n)>0], and A034460(n) = usigma(n)-n, with usigma the sum of unitary divisors of n (A034448).

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A327163 Lexicographically earliest sequence such that for all i, j, a(i) = a(j) => f(i) = f(j), where f(n) = gcd(n,usigma(n)) * (-1)^[gcd(n,usigma(n))==n], and usigma is the sum of unitary divisors of n (A034448).

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A328767 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where for n>1, f(n) = [A003415(i), A328382(i)], and f(1) = 1.

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A373380 Lexicographically earliest infinite sequence such that a(i) = a(j) => A373145(i) = A373145(j), A373362(i) = A373362(j), and A373364(i) = A373364(j), for all i, j >= 1.

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