A320113 -id:A320113 - cp's OEIS frontend

A320115 Filter sequence for counting the residue classes mod 4 of divisors of n.

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

Offset: 1

Antti Karttunen, Oct 06 2018

nonn

Restricted growth sequence transform of A320114.
For all i, j:
  A319994(i) = A319994(j) => a(i) = a(j),
  A320004(i) = A320004(j) => a(i) = a(j),
  a(i) = a(j) => A002654(i) = A002654(j).

Antti Karttunen, Table of n, a(n) for n = 1..100000

Cf. A319994, A320004, A320109, A320113, A320114, A320117.

up_to = 100000;
A320114(n) = { my(m=1); fordiv(n,d,if(d>1, m *= prime(1+(d%4)))); (m); };
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; };
v320115 = rgs_transform(vector(up_to,n,A320114(n)));
A320115(n) = v320115[n];

A320117 Filter sequence for counting the residue classes mod 6 of divisors of n.

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, Oct 06 2018

nonn

Restricted growth sequence transform of A320116.
For all i, j:
  A319717(i) = A319717(j) => a(i) = a(j),
  A319996(i) = A319996(j) => a(i) = a(j),
  A320113(i) = A320113(j) => a(i) = a(j),
  a(i) = a(j) => A002324(i) = A002324(j).

Antti Karttunen, Table of n, a(n) for n = 1..100000

Cf. A319717, A319996, A320109, A320113, A320115, A320116.

up_to = 100000;
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; };
A320116(n) = { my(m=1); fordiv(n,d,if(d>1, m *= prime(1+(d%6)))); (m); };
v320117 = rgs_transform(vector(up_to,n,A320116(n)));
A320117(n) = v320117[n];

A320109 Filter sequence for counting the residue classes mod 8 of divisors of n.

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, Oct 06 2018

nonn

Restricted growth sequence transform of A320108.

For all i, j: a(i) = a(j) => A320115(i) = A320115(j).

Antti Karttunen, Table of n, a(n) for n = 1..100000

Cf. A320108, A320113, A320115, A320117.

up_to = 100000;
A320108(n) = { my(m=1); fordiv(n,d,if(d>1, m *= prime(1+(d%8)))); (m); };
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; };
v320109 = rgs_transform(vector(up_to,n,A320108(n)));
A320109(n) = v320109[n];

A320112 a(n) = Product_{d|n, d>1} prime(1+(d mod 12)).

Original entry on oeis.org

1, 5, 7, 55, 13, 595, 19, 1265, 203, 2015, 37, 13090, 3, 475, 637, 13915, 13, 293335, 19, 509795, 3857, 5735, 37, 602140, 39, 75, 1421, 57475, 13, 28534415, 19, 320045, 7511, 2015, 9139, 12906740, 3, 475, 147, 128978135, 13, 27866825, 19, 1450955, 535717, 5735, 37, 13247080, 57, 30225, 637, 9075, 13, 34906865, 9139, 30404275, 3857, 2015, 37

Offset: 1

Antti Karttunen, Oct 06 2018

nonn

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

Cf. A319985, A320108, A320114, A320116.

Cf. A320113 (rgs-transform).

A320112(n) = { my(m=1); fordiv(n,d,if(d>1, m *= prime(1+(d%12)))); (m); };

a(n) = Product_{d|n, d>1} prime(1+(d mod 12)).

cp's OEIS Frontend

A320115 Filter sequence for counting the residue classes mod 4 of divisors of n.

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A320117 Filter sequence for counting the residue classes mod 6 of divisors of n.

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A320109 Filter sequence for counting the residue classes mod 8 of divisors of n.

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A320112 a(n) = Product_{d|n, d>1} prime(1+(d mod 12)).

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