A318837 -id:A318837 - cp's OEIS frontend

A318836 Product_{d|n, dA007431(d) > 0} prime(A007431(d)), where A007431 is the Möbius transform of Euler's totient function.

1, 2, 2, 2, 2, 4, 2, 4, 4, 10, 2, 8, 2, 22, 20, 12, 2, 28, 2, 20, 44, 46, 2, 48, 10, 62, 28, 44, 2, 100, 2, 84, 92, 94, 110, 112, 2, 118, 124, 300, 2, 484, 2, 92, 700, 146, 2, 1008, 22, 530, 188, 124, 2, 1036, 230, 1452, 236, 206, 2, 2000, 2, 218, 3388, 1596, 310, 2116, 2, 188, 292, 5170, 2, 7056, 2, 298, 5300, 236, 506

Offset: 1

Antti Karttunen, Sep 05 2018

nonn

Antti Karttunen, Table of n, a(n) for n = 1..4096

Cf. A007431, A062790, A318837 (rgs-transform).

Cf. also A318838.

A007431(n) = sumdiv(n,d,moebius(n/d)*eulerphi(d));
A318836(n) = { my(m=1); fordiv(n,d,if((dA007431(d)!=0),m *= prime(A007431(d)))); (m); };

a(n) = product_{d|n, dA008578(1+A007431(d)).

For all n >= 1, A056239(a(n)) = A062790(n).

A318839 Restricted growth sequence transform of A318838.

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, Sep 05 2018

nonn

For all i, j: a(i) = a(j) => A000010(i) = A000010(j).

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

Cf. A000010, A007431, A318838.

Cf. also A318837.

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; };
A007431(n) = sumdiv(n,d,moebius(n/d)*eulerphi(d));
A318838(n) = { my(m=1); fordiv(n,d,if((A007431(d)!=0),m *= prime(A007431(d)))); (m); };
v318839 = rgs_transform(vector(up_to,n,A318838(n)));
A318839(n) = v318839[n];

cp's OEIS Frontend

A318836 Product_{d|n, dA007431(d) > 0} prime(A007431(d)), where A007431 is the Möbius transform of Euler's totient function.

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