A318891 -id:A318891 - cp's OEIS frontend

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

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

Antti Karttunen, Sep 16 2018

nonn

Restricted growth sequence transform of A286454.

For all i, j: a(i) = a(j) => A318891(i) = A318891(j).

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

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

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];

A328469 Lexicographically earliest infinite sequence such that a(i) = a(j) => A020639(i) = A020639(j) and A046523(i) = A046523(j) for all i, j.

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, Oct 19 2019

nonn

Restricted growth sequence transform of the ordered pair [A020639(n), A046523(n)], where A020639(n) gives the smallest prime factor of n, while A046523(n) gives the prime signature of n.

For all i, j: a(i) = a(j) => A291761(i) = A291761(j).

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

Cf. A020639, A046523.

Cf. also A101296, A291761, A328470, A328477, A318891, A286455.

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; };
A020639(n) = if(n>1, if(n>n=factor(n, 0)[1, 1], n, factor(n)[1, 1]), 1);
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
Aux328469(n) = [A020639(n), A046523(n)];
v328469 = rgs_transform(vector(up_to, n, Aux328469(n)));
A328469(n) = v328469[n];

A331298 Lexicographically earliest infinite sequence such that a(i) = a(j) => A001222(i) = A001222(j) and A061395(i) = A061395(j) for all i, j.

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, Jan 18 2020

nonn

Restricted growth sequence transform of the ordered pair [A001222(n), A061395(n)].
For all i, j:
  A318891(i) = A318891(j) => a(i) = a(j),
  a(i) = a(j) => A331297(i) = A331297(j) => A326846(i) = A326846(j),
  a(i) = a(j) => A331281(i) = A331281(j),
  a(i) = a(j) => A331282(i) = A331282(j).

Antti Karttunen, Table of n, a(n) for n = 1..65537
Index entries for sequences computed from indices in prime factorization

Cf. A001222, A061395, A318891, A326846, A331281, A331282.

Cf. also A331297, A331299.

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; };
A061395(n) = if(1==n, 0, primepi(vecmax(factor(n)[, 1])));
Aux331298(n) = [bigomega(n),A061395(n)];
v331298 = rgs_transform(vector(up_to, n, Aux331298(n)));
A331298(n) = v331298[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

Antti Karttunen, Jul 12 2020

nonn

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).

Antti Karttunen, Table of n, a(n) for n = 1..65537
Index entries for sequences computed from indices in prime factorization

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.

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];

cp's OEIS Frontend

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

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A328469 Lexicographically earliest infinite sequence such that a(i) = a(j) => A020639(i) = A020639(j) and A046523(i) = A046523(j) for all i, j.

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A331298 Lexicographically earliest infinite sequence such that a(i) = a(j) => A001222(i) = A001222(j) and A061395(i) = A061395(j) for all i, j.

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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.

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