A296089 -id:A296089 - cp's OEIS frontend

A323368 Lexicographically earliest sequence such that a(i) = a(j) => A000035(i) = A000035(j) and A003557(i) = A003557(j) and A048250(i) = A048250(j), for all i, j.

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

Offset: 1

Antti Karttunen, Jan 12 2019

nonn

For all i, j:
  a(i) = a(j) => A007814(i) = A007814(j),
  a(i) = a(j) => A291751(i) = A291751(j),
  a(i) = a(j) => A296089(i) = A296089(j),
  a(i) = a(j) => A323238(i) = A323238(j).

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

Cf. A000035, A003557, A048250, A291750, A291751, A323238, A323369.
Differs from A296089 for the first time at n=103, where a(103)=88, while A296089(103)=56.
Cf. also A323366.

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; };
A003557(n) = { my(f=factor(n)); for(i=1, #f~, f[i, 2] = f[i, 2]-1); factorback(f); };
A048250(n) = factorback(apply(p -> p+1,factor(n)[,1]));
v323368 = rgs_transform(vector(up_to, n, [(n%2), A003557(n), A048250(n)]));
A323368(n) = v323368[n];

A296090 Filter combining the sum of divisors (A000203) and prime-signature (A101296) of n; restricted growth sequence transform of A286360.

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, Dec 07 2017

nonn

For all i, j:
  a(i) = a(j) => A286034(i) = A286034(j).
  a(i) = a(j) => A295880(i) = A295880(j).

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

Cf. A000203, A101296, A046523, A286034, A286360, A295300, A295888, A296089.

Differs from related A295880 for the first time at n=135, where a(135) = 123, while A295880(135) = 104.

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; };
write_to_bfile(start_offset,vec,bfilename) = { for(n=1, length(vec), write(bfilename, (n+start_offset)-1, " ", vec[n])); }
A000203(n) = sigma(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
A286360(n) = (1/2)*(2 + ((A046523(n)+A000203(n))^2) - A046523(n) - 3*A000203(n));
write_to_bfile(1,rgs_transform(vector(up_to,n,A286360(n))),"b296090.txt");

A296088 Filter combining sigma(n) with the parity of n; restricted growth sequence transform of ((-1)^n)*A000203(n).

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, Dec 07 2017

nonn

			For n = 21 and 31 the restricted growth sequence transform assigns the same value (we have a(21) = a(31) = 21) because both numbers are odd, and the sum of their divisors is equal as sigma(21) = sigma(31) = 32.
On the other hand, although sigma(14) = sigma(15) = 24, a(14) != a(15) because the other number is even and the other number is odd. Compare to A286603.

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

Cf. A000035, A000203, A286603, A291761, A296089.

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; };
write_to_bfile(start_offset,vec,bfilename) = { for(n=1, length(vec), write(bfilename, (n+start_offset)-1, " ", vec[n])); }
write_to_bfile(1,rgs_transform(vector(up_to,n,((-1)^n)*sigma(n))),"b296088.txt");

A369259 Lexicographically earliest infinite sequence such that a(i) = a(j) => A003557(i) = A003557(j), A048250(i) = A048250(j) and A342671(i) = A342671(j), for all i, j >= 1.

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, Jan 25 2024

nonn

Restricted growth sequence transform of the triplet [A003557(j), A048250(i), A342671(n)].
For all i, j >= 1:
  a(i) = a(j) => A323368(i) = A323368(j) => A291751(i) = A291751(j),
  a(i) = a(j) => A369260(i) = A369260(j) => A286603(i) = A286603(j).

Cf. A000203, A001615, A003557, A003961, A048250, A286603, A291751, A369260.

Differs from related A296089 and A323368 for the first time at n=79, where a(79) = 69, while A296089(79) = A323368(79) = 51.

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; };
A003557(n) = (n/factorback(factor(n)[, 1]));
A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A048250(n) = if(n<1, 0, sumdiv(n, d, if(core(d)==d, d)));
A342671(n) = gcd(sigma(n), A003961(n));
Aux369259(n) = [A003557(n), A048250(n), A342671(n)];
v369259 = rgs_transform(vector(up_to, n, Aux369259(n)));
A369259(n) = v369259[n];

cp's OEIS Frontend

A323368 Lexicographically earliest sequence such that a(i) = a(j) => A000035(i) = A000035(j) and A003557(i) = A003557(j) and A048250(i) = A048250(j), for all i, j.

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A296090 Filter combining the sum of divisors (A000203) and prime-signature (A101296) of n; restricted growth sequence transform of A286360.

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A296088 Filter combining sigma(n) with the parity of n; restricted growth sequence transform of ((-1)^n)*A000203(n).

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A369259 Lexicographically earliest infinite sequence such that a(i) = a(j) => A003557(i) = A003557(j), A048250(i) = A048250(j) and A342671(i) = A342671(j), for all i, j >= 1.

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