A074389 -id:A074389 - cp's OEIS frontend

A074390 a(n) is the least number k that A074389(k) = n.

1, 6, 18, 12, 200, 42, 196, 56, 459, 950, 5203, 396, 9243, 980, 1800, 336, 19363, 270, 13357, 600, 1764, 10406, 72473, 168, 18625, 34814, 4293, 812, 145493, 1350, 15376, 992, 19602, 38726, 41615, 1836, 99937, 26714, 1521, 440, 274003, 3822, 475193

Offset: 1

Labos Elemer, Aug 23 2002

nonn

			For n = 79: a(79) = 979837 because GCD(979837,998718,961272) = 79 and 979837 is the smallest.

Amiram Eldar, Table of n, a(n) for n = 1..1000

Cf. A000005, A000010, A073815, A050399, A009195, A009194.

f[x_] := GCD[DivisorSigma[1, x], EulerPhi[x], x]; t=Table[0, {100}]; Do[s=f[n]; If[s<101&&t[[s]]==0, t[[s]]=n], {n, 1, 1000000}]; t

lista(len) = {my(v = vector(len), c = 0, k = 1, f, i); while(c < len, f = factor(k); i = gcd([k, sigma(k), eulerphi(k)]); if(i <= len && v[i] == 0, c++; v[i] = k); k++); v;} \\ Amiram Eldar, Nov 14 2024

a(n) = Min{x; GCD(x, sigma(x), phi(x)) = n} = Min{x; GCD(x, A000005(x), A000010(x)) = n}.

A318459 a(n) = gcd(n, tau(n), phi(n)), where tau = A000005 and phi = A000010.

Original entry on oeis.org

1, 1, 1, 1, 1, 2, 1, 4, 3, 2, 1, 2, 1, 2, 1, 1, 1, 6, 1, 2, 1, 2, 1, 8, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 1, 8, 1, 2, 1, 2, 3, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 8, 1, 2, 1, 4, 1, 2, 3, 1, 1, 2, 1, 2, 1, 2, 1, 12, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 12, 1, 2, 1, 8, 1, 6, 1, 2, 1, 2, 1, 4, 1, 2, 3, 1, 1, 2, 1, 8, 1

Offset: 1

Antti Karttunen, Sep 07 2018, after Labos Elemer's A074389

nonn

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

Cf. A000005, A000010, A009191, A009195, A009213.

Cf. also A074389.

Table[GCD[n,DivisorSigma[0,n],EulerPhi[n]],{n,110}] (* Harvey P. Dale, Jul 30 2019 *)

A318459(n) = gcd([n, numdiv(n), eulerphi(n)]);

a(n) = gcd(n, A000005(n), A000010(n)).

a(n) = gcd(n,A009213(n)) = gcd(A000005(n),A009195(n)) = gcd(A000010(n),A009191(n)).

A074465 a(n) = gcd(n^2, sigma(n^2), phi(n^2)).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 39, 1, 1, 21, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 7, 39, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 7, 11, 1, 1, 1, 1

Offset: 1

Labos Elemer, Aug 23 2002

nonn

a(n) is odd because sigma(n^2) is odd;.

			For n=14: gcd(196,399,84) = 7 = a(14).

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

Cf. A000203, A002618, A065764, A074389, A074466.

Table[Apply[GCD, {w^2, DivisorSigma[1, w^2], EulerPhi[w^2]}], {w, 1, 128}]

A074465(n) = gcd([n^2, sigma(n^2), eulerphi(n^2)]); \\ Antti Karttunen, Sep 07 2018

a(n) = A074389(n^2).

A074466 a(n) = gcd(n^3, sigma(n^3), phi(n^3)).

Original entry on oeis.org

1, 1, 1, 1, 1, 24, 1, 1, 1, 20, 1, 8, 1, 8, 15, 1, 1, 3, 1, 4, 1, 8, 1, 24, 1, 4, 1, 16, 1, 1800, 1, 1, 3, 4, 25, 1, 1, 8, 1, 4, 1, 24, 1, 8, 3, 8, 1, 8, 1, 5, 9, 4, 1, 12, 1, 16, 1, 4, 1, 480, 1, 8, 1, 1, 65, 72, 1, 4, 3, 200, 1, 3, 1, 4, 5, 8, 1, 24, 1, 4, 1, 4, 1, 64, 5, 8, 3, 88, 1, 180, 7, 16, 1

Offset: 1

Labos Elemer, Aug 23 2002

nonn

			n=10: gcd[1000,2340,400] = 20 = a(10).

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

Cf. A053191, A074389, A074465, A175926.

[Gcd(n^3, Gcd(SumOfDivisors(n^3), EulerPhi(n^3))): n in [1..100]]; // Vincenzo Librandi, Sep 20 2018

Table[Apply[GCD, {w^3, DivisorSigma[1, w^3], EulerPhi[w^3]}], {w, 1, 128}]
GCD[#,DivisorSigma[1,#],EulerPhi[#]]&/@(Range[100]^3) (* Harvey P. Dale, Nov 03 2024 *)

A074466(n) = gcd([n^3, sigma(n^3), eulerphi(n^3)]); \\ Antti Karttunen, Sep 07 2018

a(n) = A074389(n^3).

A372569 Lexicographically earliest infinite sequence such that a(i) = a(j) => A009194(i) = A009194(j), A009195(i) = A009195(j) and A009223(i) = A009223(j), for all i, j >= 1.

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, May 25 2024

nonn

Restricted growth sequence transform of the triple [A009194(n), A009195(n), A009223(n)].

For all i, j: A372570(i) = A372570(j) => a(i) = a(j) => A074389(i) = A074389(j).

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

Cf. A009194, A009195, A009223.

Cf. also A372570, A372572.

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; };
Aux372569(n) = [gcd(n, sigma(n)), gcd(n, eulerphi(n)), gcd(eulerphi(n), sigma(n))];
v372569 = rgs_transform(vector(up_to, n, Aux372569(n)));
A372569(n) = v372569[n];

cp's OEIS Frontend

A074390 a(n) is the least number k that A074389(k) = n.

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A318459 a(n) = gcd(n, tau(n), phi(n)), where tau = A000005 and phi = A000010.

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A074465 a(n) = gcd(n^2, sigma(n^2), phi(n^2)).

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A074466 a(n) = gcd(n^3, sigma(n^3), phi(n^3)).

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A372569 Lexicographically earliest infinite sequence such that a(i) = a(j) => A009194(i) = A009194(j), A009195(i) = A009195(j) and A009223(i) = A009223(j), for all i, j >= 1.

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