A305973 -id:A305973 - cp's OEIS frontend

A305982 a(n) = Product_{d|n, dA305793(1+d)-1), where A305973(k) records the prime signature of 2k-1.

1, 2, 2, 4, 2, 8, 2, 12, 4, 8, 2, 48, 2, 20, 8, 24, 2, 32, 2, 120, 20, 8, 2, 288, 4, 28, 8, 120, 2, 320, 2, 120, 8, 20, 20, 576, 2, 20, 28, 480, 2, 320, 2, 264, 32, 8, 2, 4320, 10, 200, 20, 168, 2, 320, 8, 1200, 20, 8, 2, 11520, 2, 44, 80, 600, 28, 704, 2, 300, 8, 800, 2, 6912, 2, 44, 80, 300, 20, 448, 2, 31200, 40, 8, 2, 72000, 20, 20, 8

Offset: 1

Antti Karttunen, Jun 15 2018

nonn

Antti Karttunen, Table of n, a(n) for n = 1..8192

Cf. A305973, A305983 (rgs-transform), A305984.

A305982(n) = { my(m=1); fordiv(n, d, if((dA305973(1+d)-1))); (m); }; \\ Needs also code from A305973.

a(n) = Product_{d|n, dA008578(A305793(1+d)).

A305984 a(n) = Product_{d|n, d>1} prime(A305793(1+d)-1), where A305973(k) records the prime signature of 2k-1.

Original entry on oeis.org

1, 2, 2, 6, 2, 8, 5, 12, 4, 20, 2, 72, 7, 20, 8, 60, 5, 32, 5, 120, 20, 44, 2, 432, 10, 28, 20, 300, 2, 320, 11, 300, 8, 50, 20, 576, 11, 50, 28, 3120, 2, 800, 5, 264, 80, 20, 5, 4320, 55, 200, 20, 1428, 2, 320, 20, 1200, 50, 44, 5, 17280, 5, 154, 80, 1500, 28, 1760, 19, 300, 8, 2000, 5, 17280, 11, 44, 80, 1650, 50, 448, 5, 78000, 40, 68, 2

Offset: 1

Antti Karttunen, Jun 15 2018

nonn

Antti Karttunen, Table of n, a(n) for n = 1..8192

Cf. A305973, A305982, A305985 (rgs-transform).

A305984(n) = { my(m=1); fordiv(n, d, if((d>1), m *= prime(A305973(1+d)-1))); (m); }; \\ Needs also code from A305973.

a(n) = Product_{d|n, d>1} A008578(A305793(1+d)).

A305985 Filter sequence combining from all divisors d > 1 of n, the prime signature of 2d+1.

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, Jun 15 2018

nonn

Restricted growth sequence transform of A305984.

For all i, j: a(i) = a(j) => A086668(i) = A086668(j).

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

Cf. A305810, A305973, A305983, A305984.

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; };
A305984(n) = { my(m=1); fordiv(n, d, if((d>1), m *= prime(A305973(1+d)-1))); (m); }; \\ Needs also code from A305973.
v305985 = rgs_transform(vector(up_to,n,A305984(n)));
A305985(n) = v305985[n];

A305978 Filter sequence combining prime signatures of n and 2n+1.

Original entry on oeis.org

1, 2, 2, 3, 2, 4, 5, 6, 7, 8, 2, 9, 10, 4, 4, 11, 5, 12, 5, 12, 4, 13, 2, 14, 15, 4, 16, 17, 2, 18, 19, 20, 4, 8, 4, 21, 19, 8, 4, 22, 2, 23, 5, 12, 17, 8, 5, 24, 25, 12, 4, 26, 2, 27, 8, 27, 8, 13, 5, 28, 5, 29, 12, 30, 4, 23, 31, 12, 4, 23, 5, 32, 19, 4, 12, 33, 8, 18, 5, 34, 35, 36, 2, 28, 13, 4, 13, 37, 2, 38, 8, 17, 8, 39, 4, 40, 41, 12, 12, 42, 5, 23

Offset: 1

Antti Karttunen, Jun 15 2018

nonn

Restricted growth sequence transform of A286258.

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

Cf. A046523, A101296, A286258, A305810, A305973, A305977.

Cf. A005384 (positions of 2's), A234095 (of 5's).

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
Aux305978(n) = [A046523(n),A046523(n+n+1)];
v305978 = rgs_transform(vector(up_to,n,Aux305978(n)));
A305978(n) = v305978[n];

A305983 Filter sequence combining from all proper divisors d of n, the prime signature of 2d+1.

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, Jun 15 2018

nonn

Restricted growth sequence transform of A305982.

For all i, j: a(i) = a(j) => A305818(i) = A305818(j).

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

Cf. A305973, A305982, A305985.

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; };
A305982(n) = { my(m=1); fordiv(n, d, if((dA305973(1+d)-1))); (m); }; \\ Needs also code from A305973.
v305983 = rgs_transform(vector(up_to,n,A305982(n)));
A305983(n) = v305983[n];

A305977 Filter sequence combining prime signatures of n and 2n-1.

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, Jun 15 2018

nonn

Restricted growth sequence transform of A286257.

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

Cf. A046523, A101296, A286257, A305973, A305978.

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
Aux305977(n) = [A046523(n),A046523(n+n-1)];
v305977 = rgs_transform(vector(up_to,n,Aux305977(n)));
A305977(n) = v305977[n];

cp's OEIS Frontend

A305982 a(n) = Product_{d|n, dA305793(1+d)-1), where A305973(k) records the prime signature of 2k-1.

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Formula

A305984 a(n) = Product_{d|n, d>1} prime(A305793(1+d)-1), where A305973(k) records the prime signature of 2k-1.

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A305985 Filter sequence combining from all divisors d > 1 of n, the prime signature of 2d+1.

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A305978 Filter sequence combining prime signatures of n and 2n+1.

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A305983 Filter sequence combining from all proper divisors d of n, the prime signature of 2d+1.

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PARI

A305977 Filter sequence combining prime signatures of n and 2n-1.

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PARI