A326193 -id:A326193 - cp's OEIS frontend

A326192 Lexicographically earliest sequence such that for all i, j, a(i) = a(j) => A009195(i) = A009195(j) and f(i) = f(j), where f(n) = gcd(n,sigma(n)) * (-1)^[gcd(n,sigma(n))==n] and A009195(n) = gcd(n, phi(n)).

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

Offset: 1

Antti Karttunen, Aug 24 2019

nonn

Restricted growth sequence transform of the ordered pair [A009195(n), A326193(n)].
For all i, j:
  A305800(i) = A305800(j) => a(i) = a(j),
  a(i) = a(j) => A300242(i) = A300242(j),
  a(i) = a(j) => A326196(i) = A326196(j).

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

Cf. A009194, A009195, A300242, A305800, A326193, A326194, A326196.

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; };
Aux326192(n) = { my(u=gcd(n,sigma(n))); [gcd(n,eulerphi(n)), u*((-1)^(u==n))]; };
v326192 = rgs_transform(vector(up_to, n, Aux326192(n)));
A326192(n) = v326192[n];

A327163 Lexicographically earliest sequence such that for all i, j, a(i) = a(j) => f(i) = f(j), where f(n) = gcd(n,usigma(n)) * (-1)^[gcd(n,usigma(n))==n], and usigma is the sum of unitary divisors of n (A034448).

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, Aug 28 2019

nonn

Restricted growth sequence transform of function f, defined as f(n) = -A323166(n) = -n when n is one of unitary multiply-perfect numbers (A327158), otherwise f(n) = A323166(n) = gcd(n,A034448(n))
For all i, j:
  A305800(i) = A305800(j) => a(i) = a(j) => A327164(i) = A327164(j).

Antti Karttunen, Table of n, a(n) for n = 1..87360

Cf. A034448, A305800, A323166, A327158, A327164.

Cf. also A326193.

up_to = 87360;
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; };
A034448(n) = { my(f=factorint(n)); prod(k=1, #f~, 1+(f[k, 1]^f[k, 2])); }; \\ After code in A034448
A323166(n) = gcd(n, A034448(n));
Aux327163(n) = { my(u=A323166(n)); u*((-1)^(u==n)); };
v327163 = rgs_transform(vector(up_to, n, Aux327163(n)));
A327163(n) = v327163[n];

cp's OEIS Frontend

A326192 Lexicographically earliest sequence such that for all i, j, a(i) = a(j) => A009195(i) = A009195(j) and f(i) = f(j), where f(n) = gcd(n,sigma(n)) * (-1)^[gcd(n,sigma(n))==n] and A009195(n) = gcd(n, phi(n)).

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