A355831 -id:A355831 - cp's OEIS frontend

A355830 Lexicographically earliest infinite sequence such that a(i) = a(j) => A046523(i) = A046523(j) and A345000(i) = A345000(j) for all i, j >= 1.

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

Offset: 1

Antti Karttunen, Jul 20 2022

nonn

Restricted growth sequence transform of the ordered pair [A046523(n), A345000(n)].

For all i, j: A351235(i) = A351235(j) => a(i) = a(j).

Antti Karttunen, Table of n, a(n) for n = 1..65537
Index entries for sequences related to primorial base

Cf. A003415, A046523, A276086, A345000.

Cf. also A351235, A355000, A355831, A355832, A355836.

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]));
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A345000(n) = gcd(A003415(n),A003415(A276086(n)));
Aux355830(n) = [A046523(n), A345000(n)];
v355830 = rgs_transform(vector(up_to,n,Aux355830(n)));
A355830(n) = v355830[n];

A355000 Lexicographically earliest infinite sequence such that a(i) = a(j) => A046523(i) = A046523(j) and A327858(i) = A327858(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, 8, 2, 12, 13, 7, 2, 14, 15, 16, 5, 8, 2, 17, 2, 18, 19, 7, 20, 21, 2, 22, 10, 14, 2, 17, 2, 12, 12, 23, 2, 24, 25, 26, 13, 27, 2, 14, 10, 14, 10, 7, 2, 28, 2, 9, 12, 29, 30, 17, 2, 12, 10, 17, 2, 31, 2, 9, 32, 32, 30, 17, 2, 33, 34, 7, 2, 28, 10, 16, 10, 35, 2, 28, 10, 12, 10, 36, 20, 37, 2, 27, 26, 38, 2, 39, 2, 14, 17

Offset: 1

Antti Karttunen, Jul 19 2022

Restricted growth sequence transform of the ordered pair [A046523(n), A327858(n)].

For all i, j: A351235(i) = A351235(j) => a(i) = a(j).

Antti Karttunen, Table of n, a(n) for n = 1..65537
Index entries for sequences related to primorial base

Cf. A003415, A046523, A276086, A327858, A351235.

Cf. also A355830, A355831, A355836.

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) = {my(fac); if(n<1, 0, fac=factor(n); sum(i=1, matsize(fac)[1], n*fac[i, 2]/fac[i, 1]))}; \\ From A003415
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
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));
Aux355000(n) = [A046523(n), A327858(n)];
v355000 = rgs_transform(vector(up_to,n,Aux355000(n)));
A355000(n) = v355000[n];

A355832 Lexicographically earliest infinite sequence such that a(i) = a(j) => A354347(i) = A354347(j) for all i, j >= 1.

Original entry on oeis.org

1, 2, 2, 2, 2, 1, 2, 2, 3, 1, 2, 1, 2, 1, 1, 4, 2, 5, 2, 1, 6, 1, 2, 1, 7, 6, 3, 1, 2, 2, 2, 8, 1, 1, 2, 9, 2, 1, 1, 10, 2, 11, 2, 2, 3, 6, 2, 12, 3, 13, 6, 11, 2, 14, 1, 10, 1, 1, 2, 2, 2, 1, 15, 16, 2, 2, 2, 1, 1, 10, 2, 17, 2, 1, 18, 19, 2, 11, 2, 20, 3, 1, 2, 10, 1, 6, 1, 21, 2, 14, 1, 22, 1, 23, 2, 24, 2, 9, 3, 25, 2, 1, 2, 26, 26

Offset: 1

Antti Karttunen, Jul 19 2022

nonn

Restricted growth sequence transform of A354347, which is the Dirichlet inverse of A345000(n) = gcd(A003415(n), A003415(A276086(n))).

Antti Karttunen, Table of n, a(n) for n = 1..65537
Index entries for sequences related to primorial base

Cf. A003415, A276086, A345000, A354347, A355831.

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); };
A345000(n) = gcd(A003415(n),A003415(A276086(n)));
v354347 = DirInverseCorrect(vector(up_to,n,A345000(n)));
v355832 = rgs_transform(v354347);
A355832(n) = v355832[n];

cp's OEIS Frontend

A355830 Lexicographically earliest infinite sequence such that a(i) = a(j) => A046523(i) = A046523(j) and A345000(i) = A345000(j) for all i, j >= 1.

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A355000 Lexicographically earliest infinite sequence such that a(i) = a(j) => A046523(i) = A046523(j) and A327858(i) = A327858(j) for all i, j >= 1.

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A355832 Lexicographically earliest infinite sequence such that a(i) = a(j) => A354347(i) = A354347(j) for all i, j >= 1.

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