A318839 -id:A318839 - cp's OEIS frontend

A318838 Product_{d|n, A007431(d) > 0} prime(A007431(d)), where A007431 is the Möbius transform of Euler's totient function.

2, 2, 4, 4, 10, 4, 22, 12, 28, 10, 46, 16, 62, 22, 100, 84, 94, 28, 118, 100, 484, 46, 146, 144, 530, 62, 1036, 484, 206, 100, 218, 1596, 2116, 94, 5170, 784, 298, 118, 3844, 3900, 334, 484, 358, 2116, 25900, 146, 394, 7056, 3322, 530, 8836, 3844, 466, 1036, 23690, 42108, 13924, 206, 538, 10000, 554, 218, 240548

Offset: 1

Antti Karttunen, Sep 05 2018

nonn

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

Cf. A000010, A007431, A318839 (rgs-transform).

Cf. also A318836.

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); };

a(n) = product_{d|n} A008578(1+A007431(d)).

For all n >= 1, A056239(a(n)) = A000010(n).

A318893 Filter sequence combining the prime signature of n (A046523) with Euler totient function (A000010).

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, 23, 24, 25, 21, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 34, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 42, 48, 43, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 53, 70, 59, 71, 66, 72, 73, 74, 51, 75, 76, 77, 78, 79, 80, 81, 76, 82, 83, 71

Offset: 1

Antti Karttunen, Sep 16 2018

nonn

Restricted growth sequence transform of A286160.

For all i, j: a(i) = a(j) => A062355(i) = A062355(j).

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

Cf. A000010, A046523, A286160, A318839, A318892.

Cf. also A061468, A062355.

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; };
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
A318893aux(n) = [eulerphi(n), A046523(n)];
v318893 = rgs_transform(vector(up_to,n,A318893aux(n)));
A318893(n) = v318893[n];

A318892 Filter sequence combining the prime signature of n (A046523) with A289625.

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, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 35, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 44, 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, 68, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 75, 90

Offset: 1

Antti Karttunen, Sep 16 2018

nonn

Restricted growth sequence transform of A289628.

For all i, j: a(i) = a(j) => A318893(i) = A318893(j).

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

Cf. A046523, A289625, A289628, A318839, A318893.

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; };
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
A289625(n) = { my(m=1,p=2,v=znstar(n)[2]); for(i=1,length(v),m *= p^v[i]; p = nextprime(p+1)); (m); };
A318892aux(n) = [A046523(n), A289625(n)];
v318892 = rgs_transform(vector(up_to,n,A318892aux(n)));
A318892(n) = v318892[n];

cp's OEIS Frontend

A318838 Product_{d|n, A007431(d) > 0} prime(A007431(d)), where A007431 is the Möbius transform of Euler's totient function.

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A318893 Filter sequence combining the prime signature of n (A046523) with Euler totient function (A000010).

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A318892 Filter sequence combining the prime signature of n (A046523) with A289625.

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PARI