A324400 -id:A324400 - cp's OEIS frontend

A336920 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = [A329697(n), A331410(n), A336158(n)], for all i, j >= 1.

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

Offset: 1

Antti Karttunen, Aug 10 2020

nonn

Restricted growth sequence transform of the triplet [A329697(n), A331410(n), A336158(n)].
For all i, j:
  A324400(i) = A324400(j) => A003602(i) = A003602(j) => a(i) = a(j),
  a(i) = a(j) => A335880(i) = A335880(j),
  a(i) = a(j) => A336391(i) = A336391(j),
  a(i) = a(j) => A336471(i) = A336471(j).

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

Cf. A000265, A003602, A324400, A329697, A331410, A335880, A336391, A336471.

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; };
A000265(n) = (n>>valuation(n,2));
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
A336158(n) = A046523(A000265(n));
A329697(n) = if(!bitand(n,n-1),0,1+A329697(n-(n/vecmax(factor(n)[, 1]))));
A331410(n) = if(!bitand(n,n-1),0,1+A331410(n+(n/vecmax(factor(n)[, 1]))));
Aux336920(n) = [A329697(n), A331410(n), A336158(n)];
v336920 = rgs_transform(vector(up_to, n, Aux336920(n)));
A336920(n) = v336920[n];

A336925 Lexicographically earliest infinite sequence such that a(i) = a(j) => A336147(1+sigma(i)) = A336147(1+sigma(j)), for all i, j >= 1.

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, Aug 10 2020

nonn

Restricted growth sequence transform of the function f(n) = A336147(A088580(n)).
For all i, j:
  A324400(i) = A324400(j) => a(i) = a(j),
  a(i) = a(j) => A336691(i) = A336691(j),
  a(i) = a(j) => A336924(i) = A336924(j).

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

Cf. also A336926.

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; };
A020639(n) = if(1==n, n, factor(n)[1, 1]);
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
A122111(n) = if(1==n,n,my(f=factor(n), es=Vecrev(f[,2]),is=concat(apply(primepi,Vecrev(f[,1])),[0]),pri=0,m=1); for(i=1, #es, pri += es[i]; m *= prime(pri)^(is[i]-is[1+i])); (m));
A278221(n) = A046523(A122111(n));
Aux336147(n) = [A020639(n),A278221(n)];
v336925 = rgs_transform(vector(up_to, n, Aux336147(1+sigma(n))));
A336925(n) = v336925[n];

A337200 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278222(A337194(i)) = A278222(A337194(j)), for all i, j >= 1.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 1, 1, 1, 1, 1, 1, 3, 3, 4, 5, 1, 3, 1, 1, 1, 5, 4, 1, 1, 3, 1, 1, 1, 2, 1, 6, 3, 1, 1, 6, 5, 1, 4, 5, 3, 3, 1, 1, 6, 7, 3, 5, 2, 1, 3, 1, 4, 6, 1, 5, 1, 1, 2, 1, 5, 3, 3, 1, 1, 3, 3, 5, 5, 6, 1, 3, 1, 5, 4, 7, 7, 1, 5, 1, 2, 3, 1, 6, 6, 8, 1, 5, 1, 3, 1, 1, 5, 9, 3, 10, 5, 2, 2, 9, 1

Offset: 1

Antti Karttunen, Aug 20 2020

nonn

Restricted growth sequence transform of f(n) = A278222(A337194(n)).

For all i, j: A324400(i) = A324400(j) => a(i) = a(j) => A337199(i) = A337199(j).

Cf. A000203, A000265, A278222, A161942, A336698, A337194, A337199.

Cf. also A286622, A324400, A337201.

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; };
A000265(n) = (n>>valuation(n, 2));
A337194(n) = (1+A000265(sigma(n)));
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
A278222(n) = A046523(A005940(1+n));
v337200 = rgs_transform(vector(up_to, n, A278222(A337194(n))));
A337200(n) = v337200[n];

A337201 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278221(A337194(i)) = A278221(A337194(j)), for all i, j >= 1.

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, Aug 20 2020

nonn

Restricted growth sequence transform of f(n) = A278221(A337194(n)).

For all i, j: A324400(i) = A324400(j) => a(i) = a(j) => A337198(i) = A337198(j).

Cf. A000203, A000265, A278221, A161942, A336698, A337194, A337198.

Cf. also A286621, A324400, A337200.

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; };
A000265(n) = (n>>valuation(n, 2));
A337194(n) = (1+A000265(sigma(n)));
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
A122111(n) = if(1==n,n,my(f=factor(n), es=Vecrev(f[,2]),is=concat(apply(primepi,Vecrev(f[,1])),[0]),pri=0,m=1); for(i=1, #es, pri += es[i]; m *= prime(pri)^(is[i]-is[1+i])); (m));
A278221(n) = A046523(A122111(n));
v337201 = rgs_transform(vector(up_to, n, A278221(A337194(n))));
A337201(n) = v337201[n];

A336648 Lexicographically earliest infinite sequence such that a(i) = a(j) => A336476(i) = A336476(j), for all i, j >= 1.

Original entry on oeis.org

1, 1, 2, 1, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 3, 1, 2, 1, 2, 2, 4, 2, 2, 2, 1, 2, 4, 2, 2, 3, 2, 1, 3, 2, 4, 1, 2, 2, 4, 2, 2, 4, 2, 2, 5, 2, 2, 2, 6, 1, 3, 2, 2, 4, 4, 2, 4, 2, 2, 3, 2, 2, 2, 1, 4, 3, 2, 2, 3, 4, 2, 1, 2, 2, 2, 2, 4, 4, 2, 2, 1, 2, 2, 4, 4, 2, 3, 2, 2, 5, 7, 2, 4, 2, 8, 2, 2, 6, 5, 1, 2, 3, 2, 2, 9

Offset: 1

Antti Karttunen, Jul 31 2020

nonn

Restricted growth sequence transform of A336476.

For all i, j: A324400(i) = A324400(j) => A003602(i) = A003602(j) => a(i) = a(j).

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

Cf. A000593, A336475, A336476.

Cf. also A003602, A324400, A336320.

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; };
A000593(n) = sigma(n>>valuation(n, 2));
A336475(n) = { my(f=factor(n)); prod(i=1, #f~, if(2==f[i,1],1,(1+f[i,2]) * (f[i,1]^f[i,2]))); };
A336476(n) = gcd(A000593(n), A336475(n));
v336648 = rgs_transform(vector(up_to,n,A336476(n)));
A336648(n) = v336648[n];

A344180 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j) for all i, j >= 0, where f(n) = 0 if n is a Fibbinary number (A003714), otherwise f(n) = n.

Original entry on oeis.org

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

Offset: 0

Antti Karttunen, May 16 2021

nonn

For all i, j:
  a(i) = a(j) => A085357(i) = A085357(j),
  a(i) = a(j) => A213370(i) = A213370(j),
  a(i) = a(j) => A344182(i) = A344182(j).

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

Cf. A003714 (positions of 1's), A085357, A213370, A344182.

Cf. also A324400.

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; };
Aux344180(n) = if(!bitand(n,n+n),0,n);
v344180 = rgs_transform(vector(1+up_to,n,Aux344180(n-1)));
A344180(n) = v344180[1+n];

cp's OEIS Frontend

A336920 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = [A329697(n), A331410(n), A336158(n)], for all i, j >= 1.

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A336925 Lexicographically earliest infinite sequence such that a(i) = a(j) => A336147(1+sigma(i)) = A336147(1+sigma(j)), for all i, j >= 1.

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A337200 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278222(A337194(i)) = A278222(A337194(j)), for all i, j >= 1.

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A337201 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278221(A337194(i)) = A278221(A337194(j)), for all i, j >= 1.

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A336648 Lexicographically earliest infinite sequence such that a(i) = a(j) => A336476(i) = A336476(j), for all i, j >= 1.

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A344180 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j) for all i, j >= 0, where f(n) = 0 if n is a Fibbinary number (A003714), otherwise f(n) = n.

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