A326202 -id:A326202 - cp's OEIS frontend

A326200 Lexicographically earliest sequence such that a(i) = a(j) => sigma(i)/i = sigma(j)/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, 23, 24, 25, 26, 27, 6, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90

Offset: 1

Antti Karttunen, Jun 13 2019

nonn

Restricted growth sequence transform of the abundancy index of n.
For all i, j:
  a(i) = a(j) <=> A094759(i) = A094759(j),
  a(i) = a(j) => A017665(i) = A017665(j),
  a(i) = a(j) => A017666(i) = A017666(j).

Antti Karttunen, Table of n, a(n) for n = 1..105664
Achim Flammenkamp, The Multiply Perfect Numbers Page

Cf. A000396 (positions of 6's), A005820 (positions of 119's).
Cf. A017665, A017666, A074902, A094759.
Cf. A218406, A218407, A218408, A218427, A326202.

up_to = 105664; \\ (In the same equivalence class as 78, 364 and 6448).
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; };
v326200 = rgs_transform(vector(up_to,n,sigma(n)/n));
A326200(n) = v326200[n];

A326201 Lexicographically earliest sequence such that for all i, j, a(i) = a(j) => f(i) = f(j), where f(n) = 0 if n > 1 and gcd(n,A000005(n)) = 1, with f(n) = n for all other numbers.

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, Jul 11 2019

nonn

For all i, j:
  A305801(i) = A305801(j) => a(i) = a(j),
  a(i) = a(j) => A009191(i) = A009191(j) => A322980(i) = A322980(j).

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

Cf. A000005, A009191, A046642, A305801, A322980.

Cf. also A326202, A326203.

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; };
Aux326201(n) = if((n>1) && (1==gcd(n,numdiv(n))),0,n);
v326201 = rgs_transform(vector(up_to, n, Aux326201(n)));
A326201(n) = v326201[n];

A326203 Lexicographically earliest sequence such that for all i, j, a(i) = a(j) => f(i) = f(j), where f(n) = 0 if n > 2 and gcd(n,phi(n)) = 1, with f(n) = n for all other numbers.

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, Jul 11 2019

nonn

For all i, j:
  A305801(i) = A305801(j) => a(i) = a(j),
  a(i) = a(j) => A009195(i) = A009195(j) => A297086(i) = A297086(j),
  a(i) = a(j) => A000001(i) = A000001(j) => A297086(i) = A297086(j).

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

Cf. A000001, A000010, A003277, A009195, A297086, A305801.

Cf. also A326201, A326202.

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; };
Aux326203(n) = if((n>2) && (1==gcd(n,eulerphi(n))),0,n);
v326203 = rgs_transform(vector(up_to, n, Aux326203(n)));
A326203(n) = v326203[n];

cp's OEIS Frontend

A326200 Lexicographically earliest sequence such that a(i) = a(j) => sigma(i)/i = sigma(j)/j for all i, j.

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A326201 Lexicographically earliest sequence such that for all i, j, a(i) = a(j) => f(i) = f(j), where f(n) = 0 if n > 1 and gcd(n,A000005(n)) = 1, with f(n) = n for all other numbers.

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A326203 Lexicographically earliest sequence such that for all i, j, a(i) = a(j) => f(i) = f(j), where f(n) = 0 if n > 2 and gcd(n,phi(n)) = 1, with f(n) = n for all other numbers.

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PARI