A300241 -id:A300241 - cp's OEIS frontend

A300240 Filter sequence combining A009195(n) and A046523(n), i.e., gcd(n,phi(n)) and the prime signature of n.

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

Offset: 1

Antti Karttunen, Mar 02 2018

nonn

Restricted growth sequence transform of P(A009195(n), A046523(n)), where P(a,b) is a two-argument form of A000027 used as a Cantor pairing function N x N -> N.

			a(6) = a(10) (= 4) because both 6 and 10 are nonsquare semiprimes, and A009195(6) = A009195(10) = 2.

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

Cf. A009195, A046523.

Cf. also A300230, A300241, A300242, A300243.

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; };
write_to_bfile(start_offset,vec,bfilename) = { for(n=1, length(vec), write(bfilename, (n+start_offset)-1, " ", vec[n])); }
A009195(n) = gcd(n, eulerphi(n));
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
Aux300240(n) = (1/2)*(2 + ((A046523(n)+A009195(n))^2) - A046523(n) - 3*A009195(n));
write_to_bfile(1,rgs_transform(vector(65537,n,Aux300240(n))),"b300240.txt");

A300242 Filter sequence combining gcd(n,sigma(n)) and gcd(n,phi(n)), (A009194 and A009195).

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, Mar 02 2018

nonn

Restricted growth sequence transform of P(A009194(n), A009195(n)), where P(a,b) is a two-argument form of A000027 used as a Cantor pairing function N x N -> N.

			a(15) = a(33) (= 8) because A009194(15) = A009194(33) = 3 and A009195(15) = A009195(33) = 1.
a(20) = a(52) (= 11) because A009194(20) = A009194(52) = 2 and A009195(20) = A009195(52) = 4.

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

Cf. A009194, A009195.

Cf. also A286591, A300225, A300240, A300241, A300243.

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; };
write_to_bfile(start_offset,vec,bfilename) = { for(n=1, length(vec), write(bfilename, (n+start_offset)-1, " ", vec[n])); }
A009194(n) = gcd(n, sigma(n));
A009195(n) = gcd(n, eulerphi(n));
Aux300242(n) = (1/2)*(2 + ((A009194(n)+A009195(n))^2) - A009194(n) - 3*A009195(n));
write_to_bfile(1,rgs_transform(vector(65537,n,Aux300242(n))),"b300242.txt");

A300243 Filter sequence combining A051953(n) and A009195(n), n-phi(n) (cototient of n) and gcd(n,n-phi(n)).

Original entry on oeis.org

1, 2, 2, 3, 2, 4, 2, 5, 6, 7, 2, 8, 2, 9, 10, 11, 2, 12, 2, 13, 14, 15, 2, 16, 17, 18, 19, 20, 2, 21, 2, 22, 23, 24, 25, 26, 2, 27, 28, 29, 2, 30, 2, 31, 32, 33, 2, 34, 35, 36, 37, 38, 2, 39, 40, 41, 32, 42, 2, 43, 2, 44, 45, 46, 47, 48, 2, 49, 50, 48, 2, 51, 2, 52, 53, 54, 47, 55, 2, 56, 57, 58, 2, 59, 60, 61, 62, 63, 2, 64, 37, 65, 66, 67, 68, 69, 2, 70, 71

Offset: 1

Antti Karttunen, Mar 02 2018

nonn

Restricted growth sequence transform of P(A051953(n), A009195(n)), where P(a,b) is a two-argument form of A000027 used as a Cantor pairing function N x N -> N.

			a(66) = a(70) (= 48) because A051953(66) = A051953(70) = 46 and A009195(66) = A009195(70) = 2.

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

Cf. A009195, A051953.

Cf. also A300233, A300240, A300241, A300242.

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; };
write_to_bfile(start_offset,vec,bfilename) = { for(n=1, length(vec), write(bfilename, (n+start_offset)-1, " ", vec[n])); }
A009195(n) = gcd(n, eulerphi(n));
A051953(n) = (n - eulerphi(n));
Aux300243(n) = (1/2)*(2 + ((A051953(n)+A009195(n))^2) - A051953(n) - 3*A009195(n));
write_to_bfile(1,rgs_transform(vector(65537,n,Aux300243(n))),"b300243.txt");

cp's OEIS Frontend

A300240 Filter sequence combining A009195(n) and A046523(n), i.e., gcd(n,phi(n)) and the prime signature of n.

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A300242 Filter sequence combining gcd(n,sigma(n)) and gcd(n,phi(n)), (A009194 and A009195).

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A300243 Filter sequence combining A051953(n) and A009195(n), n-phi(n) (cototient of n) and gcd(n,n-phi(n)).

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