A320114 -id:A320114 - 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];

A320116 a(n) = Product_{d|n, d>1} prime(1+(d mod 6)).

Original entry on oeis.org

1, 5, 7, 55, 13, 70, 3, 275, 49, 715, 13, 1540, 3, 75, 637, 3025, 13, 980, 3, 39325, 147, 715, 13, 15400, 39, 75, 343, 9075, 13, 140140, 3, 15125, 637, 715, 507, 43120, 3, 75, 147, 2162875, 13, 14700, 3, 39325, 31213, 715, 13, 338800, 9, 10725, 637, 9075, 13, 13720, 507, 226875, 147, 715, 13, 30830800, 3, 75, 7203, 166375, 507, 140140, 3

Offset: 1

Antti Karttunen, Oct 06 2018

nonn

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

Cf. A320114, A320117 (rgs-transform),

Cf. also A319986.

A320116(n) = { my(m=1); fordiv(n,d,if(d>1, m *= prime(1+(d%6)))); (m); };

a(n) = Product_{d|n, d>1} prime(1+(d mod 6)).

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).

A320108 a(n) = Product_{d|n, d>1} prime(1+(d mod 8)).

Original entry on oeis.org

1, 5, 7, 55, 13, 595, 19, 110, 21, 325, 7, 71995, 13, 1615, 1729, 220, 3, 8925, 7, 39325, 1729, 595, 19, 287980, 39, 325, 147, 195415, 13, 12492025, 19, 440, 147, 75, 1729, 11879175, 13, 595, 1729, 157300, 3, 12492025, 7, 71995, 67431, 1615, 19, 1151920, 57, 4875, 147, 39325, 13, 1062075, 1729, 781660, 147, 325, 7, 182895738025, 13, 1615, 98553, 880, 507

Offset: 1

Antti Karttunen, Oct 06 2018

nonn

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

Cf. A080682, A319987, A320112, A320114, A320116.

Cf. A320109 (rgs-transform).

A320108(n) = { my(m=1); fordiv(n,d,if(d>1, m *= prime(1+(d%8)))); (m); };

a(n) = Product_{d|n, d>1} prime(1+(d mod 8)).

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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A320116 a(n) = Product_{d|n, d>1} prime(1+(d mod 6)).

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

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A320108 a(n) = Product_{d|n, d>1} prime(1+(d mod 8)).

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

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