cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A286621 Restricted growth sequence computed for filter-sequence A278221, related to the conjugated prime factorization (see A122111).

Original entry on oeis.org

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

Views

Author

Antti Karttunen, May 11 2017

Keywords

Comments

When filtering sequences (by equivalence class partitioning), this sequence (with its modestly sized terms) can be used instead of A278221 (which has some huge terms), because for all i, j it holds that: a(i) = a(j) <=> A278221(i) = A278221(j).
For example, for all i, j: a(i) = a(j) => A006530(i) = A006530(j).

Examples

			For n=2, A278221(2) = 2, which has not been encountered before, thus we allot for a(2) the least so far unused number, which is 2, thus a(2) = 2.
For n=3, A278221(3) = 4, which has not been encountered before, thus we allot for a(3) the least so far unused number, which is 3, thus a(3) = 3.
For n=4, A278221(4) = 2, which was already encountered as A278221(2), thus we set a(4) = a(2) = 2.
For n=9, A278221(9) = 4, which was already encountered at n=3, thus a(9) = 3.
For n=13, A278221(13) = 64, which has not been encountered before, thus we allot for a(13) the least so far unused number, which is 9, thus a(13) = 9.
For n=194, A278221(194) = 50331648, which has not been encountered before, thus we allot for a(194) the least so far unused number, which is 106, thus a(194) = 106.
For n=388, A278221(388) = 50331648, which was already encountered at n=194, thus a(388) = a(194) = 106.

Links

Crossrefs

Cf. A278221, A006530, A122111.
Cf. also A101296, A286603, A286605, A286610, A286619, A286622, A286626, A286378 for similarly constructed sequences.

Programs

  • PARI
    rgs_transform(invec) = { my(occurrences = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(occurrences,invec[i]), my(pp = mapget(occurrences, invec[i])); outvec[i] = outvec[pp] , mapput(occurrences,invec[i],i); outvec[i] = u; u++ )); outvec; };
write_to_bfile(start_offset,vec,bfilename) = { for(n=1, length(vec), write(bfilename, (n+start_offset)-1, " ", vec[n])); }
A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
A122111(n) = if(1==n,n,prime(bigomega(n))*A122111(A064989(n)));
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ This function from Charles R Greathouse IV, Aug 17 2011
A278221(n) = A046523(A122111(n));
write_to_bfile(1,rgs_transform(vector(10000,n,A278221(n))),"b286621.txt");

Formula

Construction: we start with a(1)=1 for A278221(1)=1, and then after, for all n > 1, we use the least so far unused natural number k for a(n) if A278221(n) has not been encountered before, otherwise [whenever A278221(n) = A278221(m), for some m < n], we set a(n) = a(m).

A336149 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278221(i) = A278221(j) and A278222(i) = A278222(j), for all i, j >= 1.

Original entry on oeis.org

1, 2, 3, 2, 4, 5, 6, 2, 7, 8, 9, 5, 10, 11, 12, 2, 13, 14, 15, 8, 16, 17, 18, 5, 19, 20, 21, 11, 22, 23, 24, 2, 25, 26, 27, 14, 28, 29, 30, 8, 31, 32, 33, 17, 34, 35, 36, 5, 37, 38, 39, 20, 40, 41, 42, 11, 43, 44, 45, 23, 46, 47, 48, 2, 49, 50, 51, 26, 52, 53, 54, 14, 55, 56, 34, 29, 57, 58, 59, 8, 60, 61, 62, 32, 63, 64, 65, 17, 66, 67, 68, 35, 69, 70, 71, 5, 72, 27, 73, 38, 74, 75, 76, 20, 77
Offset: 1

Views

Author

Antti Karttunen, Jul 12 2020

Keywords

Comments

Restricted growth sequence transform of the ordered pair [A278221(n), A278222(n)], i.e., of the ordered pair [A046523(A122111(n)), A046523(A005940(1+n))].
For all i, j: A336146(i) = A336146(j) => a(i) = a(j) => A035531(i) = A035531(j).

Links

Crossrefs

Cf. A005940, A046523, A064989, A122111, A278221, A278222.
Cf. also A035531, A286621, A286622, A324400, A336146, A336148, A336159.

Programs

  • PARI
    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; };
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
A122111(n) = if(1==n,n,prime(bigomega(n))*A122111(A064989(n)));
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
A278221(n) = A046523(A122111(n));
A278222(n) = A046523(A005940(1+n));
Aux336149(n) = [A278221(n),A278222(n)];
v336149 = rgs_transform(vector(up_to, n, Aux336149(n)));
A336149(n) = v336149[n];

A318890 Filter sequence combining the prime signature of n (A046523) with the prime signature of its conjugated prime factorization (A278221).

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 10, 15, 16, 12, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 14, 33, 34, 35, 36, 37, 38, 39, 40, 41, 18, 42, 43, 44, 45, 18, 46, 47, 48, 22, 31, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 39, 63, 64, 65, 66, 18, 67, 20, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 53, 36, 80, 81, 82, 83, 84, 85, 26, 86, 87, 88, 89, 90, 91, 39
Offset: 1

Views

Author

Antti Karttunen, Sep 16 2018

Keywords

Comments

Restricted growth sequence transform of A286454.
For all i, j: a(i) = a(j) => A318891(i) = A318891(j).

Links

Crossrefs

Cf. A046523, A101296, A278221, A286454, A286621, A318891.

Programs

  • PARI
    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; };
A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
A122111(n) = if(1==n,n,prime(bigomega(n))*A122111(A064989(n)));
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
A278221(n) = A046523(A122111(n));
A318890aux(n) = [A046523(n), A278221(n)];
v318890 = rgs_transform(vector(up_to,n,A318890aux(n)));
A318890(n) = v318890[n];

A336148 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278221(i) = A278221(j) and A336158(i) = A336158(j), for all i, j >= 1.

Original entry on oeis.org

1, 2, 3, 2, 4, 5, 6, 2, 7, 8, 9, 5, 10, 11, 12, 2, 13, 14, 15, 8, 16, 17, 18, 5, 19, 20, 21, 11, 22, 23, 24, 2, 25, 26, 27, 14, 28, 29, 30, 8, 31, 32, 33, 17, 34, 35, 36, 5, 37, 38, 39, 20, 40, 41, 25, 11, 42, 43, 44, 23, 45, 46, 47, 2, 48, 49, 50, 26, 51, 32, 52, 14, 53, 54, 34, 29, 55, 56, 57, 8, 58, 59, 60, 32, 61, 62, 63, 17, 64, 65, 30, 35, 66, 67, 68, 5, 69, 70, 71, 38, 72, 73, 74, 20, 75
Offset: 1

Views

Author

Antti Karttunen, Jul 12 2020

Keywords

Comments

Restricted growth sequence transform of the ordered pair [A278221(n), A336158(n)], i.e., of the ordered pair [A046523(A122111(n)), A046523(A000265(n))].
For all i, j: A324400(i) = A324400(j) => A336146(i) = A336146(j) => a(i) = a(j).

Links

Crossrefs

Cf. A000265, A046523, A064989, A122111, A278221, A336158.
Cf. also A286621, A318890, A324400, A336146, A336149, A336159.

Programs

  • PARI
    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; };
A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
A122111(n) = if(1==n,n,prime(bigomega(n))*A122111(A064989(n)));
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
A278221(n) = A046523(A122111(n));
A000265(n) = (n>>valuation(n,2));
A336158(n) = A046523(A000265(n));
Aux336148(n) = [A278221(n),A336158(n)];
v336148 = rgs_transform(vector(up_to, n, Aux336148(n)));
A336148(n) = v336148[n];

A322814 Lexicographically earliest such sequence a that a(i) = a(j) => f(i) = f(j) for all i, j, where f(2) = -1, f(n) = 0 if n is an odd prime, and f(n) = A278221(n) for all other numbers.

Original entry on oeis.org

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

Views

Author

Antti Karttunen, Dec 27 2018

Keywords

Comments

For all i, j: a(i) = a(j) => A001221(i) = A001221(j).

Links

Crossrefs

Cf. A046523, A122111, A278221, A286621, A318890.

Programs

  • PARI
    up_to = 4096;
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]); };  \\ From A046523
A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
A122111(n) = if(1==n,n,prime(bigomega(n))*A122111(A064989(n)));
A322814aux(n) = if(2==n,-1,if(isprime(n),0,A046523(A122111(n))));
v322814 = rgs_transform(vector(up_to,n,A322814aux(n)));
A322814(n) = v322814[n];

A336147 Lexicographically earliest infinite sequence such that a(i) = a(j) => A020639(i) = A020639(j) and A278221(i) = A278221(j), for all i, j >= 1.

Original entry on oeis.org

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

Views

Author

Antti Karttunen, Jul 12 2020

Keywords

Comments

Restricted growth sequence transform of the ordered pair [A020639(n), A278221(n)].
For all i, j:
A324400(i) = A324400(j) => A336146(i) = A336146(j) => a(i) = a(j),
a(i) = a(j) => A243055(i) = A243055(j),
a(i) = a(j) => A336150(i) = A336150(j).

Links

Crossrefs

Cf. A020639, A046523, A122111, A278221.
Cf. also A243055, A286621, A318891, A324400, A336146, A336148, A336149, A336150.
First differs from A322590 at a(70) = 28 instead of 44.

Programs

  • PARI
    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]);
A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
A122111(n) = if(1==n,n,prime(bigomega(n))*A122111(A064989(n)));
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
A278221(n) = A046523(A122111(n));
Aux336147(n) = [A020639(n),A278221(n)];
v336147 = rgs_transform(vector(up_to, n, Aux336147(n)));
A336147(n) = v336147[n];

A336393 Lexicographically earliest infinite sequence such that a(i) = a(j) => A336467(i) = A336467(j) and A278221(A000265(i)) = A278221(A000265(j)), for all i, j >= 1.

Original entry on oeis.org

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

Views

Author

Antti Karttunen, Aug 10 2020

Keywords

Comments

Restricted growth sequence transform of the ordered pair [A336467(n), A278221(A000265(n))], or equally, of the ordered pair [A336467(n), A336395(n)].
For all i, j:
A324400(i) = A324400(j) => A003602(i) = A003602(j) => a(i) = a(j).

Links

Crossrefs

Cf. A000265, A003602, A324400, A278221, A286621, A336390, A336395, A336467.

Programs

  • PARI
    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
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));
A336467(n) = { my(f=factor(n)); prod(k=1,#f~,if(2==f[k,1],1,(A000265(f[k,1]+1))^f[k,2])); };
Aux336393(n) = [A336467(n), A278221(A000265(n))];
v336393 = rgs_transform(vector(up_to, n, Aux336393(n)));
A336393(n) = v336393[n];

A336395 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278221(A000265(i)) = A278221(A000265(j)), for all i, j >= 1.

Original entry on oeis.org

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

Views

Author

Antti Karttunen, Aug 10 2020

Keywords

Comments

Restricted growth sequence transform of the function f(n) = A278221(A000265(n)), the prime signature of the conjugated prime factorization of the odd part of n.
For all i, j:
A324400(i) = A324400(j) => A003602(i) = A003602(j) => a(i) = a(j),
a(i) = a(j) => A005087(i) = A005087(j).

Links

Crossrefs

Cf. A000265, A003602, A005087, A278221, A286621, A324400.
Cf. also A336393.

Programs

  • PARI
    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
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));
v336395 = rgs_transform(vector(up_to, n, A278221(A000265(n))));
A336395(n) = v336395[n];

A336474 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278221(i) = A278221(j) and A329697(i) = A329697(j), for all i, j >= 1.

Original entry on oeis.org

1, 2, 3, 2, 4, 5, 6, 2, 7, 8, 9, 5, 10, 11, 12, 2, 13, 14, 15, 8, 16, 17, 18, 5, 19, 20, 21, 11, 22, 23, 24, 2, 25, 26, 27, 14, 28, 29, 30, 8, 31, 32, 33, 17, 34, 35, 36, 5, 37, 12, 38, 20, 39, 40, 25, 11, 41, 42, 43, 23, 44, 45, 46, 2, 47, 48, 49, 26, 50, 32, 51, 14, 52, 53, 34, 29, 54, 55, 56, 8, 57, 58, 59, 32, 60, 61, 62, 17, 63, 64, 65, 35, 66, 67, 68, 5, 69, 70, 71, 12, 72, 73, 74, 20, 75
Offset: 1

Views

Author

Antti Karttunen, Jul 25 2020

Keywords

Comments

Restricted growth sequence transform of the ordered pair [A278221(n), A329697(n)].
For all i, j: A324400(i) = A324400(j) => A336146(i) = A336146(j) => a(i) = a(j).

Links

Crossrefs

Cf. A046523, A122111, A278221, A329697.
Cf. also A324400, A336146, A336473.

Programs

  • PARI
    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; };
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));
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
A278221(n) = A046523(A122111(n));
A329697(n) = if(!bitand(n,n-1),0,1+A329697(n-(n/vecmax(factor(n)[, 1]))));
Aux336474(n) = [A278221(n), A329697(n)];
v336474 = rgs_transform(vector(up_to,n,Aux336474(n)));
A336474(n) = v336474[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

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Author

Antti Karttunen, Aug 20 2020

Keywords

Comments

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).

Links

Crossrefs

Cf. A000203, A000265, A278221, A161942, A336698, A337194, A337198.
Cf. also A286621, A324400, A337200.

Programs

  • PARI
    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];
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