A320115 -id:A320115 - cp's OEIS frontend

A320114 a(n) = Product_{d|n, d>1} prime(1+(d mod 4)).

1, 5, 7, 10, 3, 175, 7, 20, 21, 75, 7, 700, 3, 175, 147, 40, 3, 2625, 7, 300, 147, 175, 7, 2800, 9, 75, 147, 700, 3, 91875, 7, 80, 147, 75, 147, 21000, 3, 175, 147, 1200, 3, 91875, 7, 700, 1323, 175, 7, 11200, 21, 1125, 147, 300, 3, 91875, 147, 2800, 147, 75, 7, 1470000, 3, 175, 3087, 160, 27, 91875, 7, 300, 147, 91875, 7, 168000, 3, 75

Offset: 1

Antti Karttunen, Oct 06 2018

nonn

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

Cf. A320115 (rgs-transform), A320116.
Cf. also A319984.
Cf. A002144 (a(n)=3), A002145 (a(n)=7).

A320114(n) = { my(m=1); fordiv(n,d,if(d>1, m *= prime(1+(d%4)))); (m); };

a(n) = Product_{d|n, d>1} prime(1+(d mod 4)).

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];

A319984 Fully multiplicative with a(p^e) = prime(p mod 4)^e.

Original entry on oeis.org

1, 3, 5, 9, 2, 15, 5, 27, 25, 6, 5, 45, 2, 15, 10, 81, 2, 75, 5, 18, 25, 15, 5, 135, 4, 6, 125, 45, 2, 30, 5, 243, 25, 6, 10, 225, 2, 15, 10, 54, 2, 75, 5, 45, 50, 15, 5, 405, 25, 12, 10, 18, 2, 375, 10, 135, 25, 6, 5, 90, 2, 15, 125, 729, 4, 75, 5, 18, 25, 30, 5, 675, 2, 6, 20, 45, 25, 30, 5, 162, 625, 6, 5, 225, 4, 15, 10, 135, 2, 150, 10, 45, 25, 15, 10

Offset: 1

Antti Karttunen, Oct 06 2018

For all i, j:

A319714(i) = A319714(j) => a(i) = a(j) => A065338(i) = A065338(j).

Antti Karttunen, Table of n, a(n) for n = 1..10000
Antti Karttunen, Data supplement: n, a(n) computed for n = 1..100000

Cf. also A065338, A319714, A319985, A319986, A319987, A320114, A320115.

A319984(n) = { my(f=factor(n)); prod(i=1, #f~, (prime(f[i, 1]%4))^f[i, 2]); };

For all n, A003963(a(n)) = A065338(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];

A320113 Filter sequence for counting the residue classes mod 12 of divisors of n.

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, Oct 06 2018

nonn

Restricted growth sequence transform of A320112.
For all i, j:
  a(i) = a(j) => A320115(i) = A320115(j).
  a(i) = a(j) => A320117(i) = A320117(j).

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

Cf. A320109, A320112, A320115, A320117.

up_to = 100000;
A320112(n) = { my(m=1); fordiv(n,d,if(d>1, m *= prime(1+(d%12)))); (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; };
v320113 = rgs_transform(vector(up_to,n,A320112(n)));
A320113(n) = v320113[n];

cp's OEIS Frontend

A320114 a(n) = Product_{d|n, d>1} prime(1+(d mod 4)).

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

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A319984 Fully multiplicative with a(p^e) = prime(p mod 4)^e.

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

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PARI

A320113 Filter sequence for counting the residue classes mod 12 of divisors of n.

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PARI