A319987 -id:A319987 - cp's OEIS frontend

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

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).

A319985 Fully multiplicative with a(p^e) = prime(p mod 12)^e.

Original entry on oeis.org

1, 3, 5, 9, 11, 15, 17, 27, 25, 33, 31, 45, 2, 51, 55, 81, 11, 75, 17, 99, 85, 93, 31, 135, 121, 6, 125, 153, 11, 165, 17, 243, 155, 33, 187, 225, 2, 51, 10, 297, 11, 255, 17, 279, 275, 93, 31, 405, 289, 363, 55, 18, 11, 375, 341, 459, 85, 33, 31, 495, 2, 51, 425, 729, 22, 465, 17, 99, 155, 561, 31, 675, 2, 6, 605, 153, 527, 30, 17

Offset: 1

Antti Karttunen, Oct 06 2018

For all i, j:
  a(i) = a(j) => A319984(i) = A319984(j).
  a(i) = a(j) => A319986(i) = A319986(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. A319984, A319986, A319987.

A319985(n) = { my(f=factor(n)); prod(i=1, #f~, (prime(f[i, 1]%12))^f[i, 2]); };

A319986 Fully multiplicative with a(p^e) = prime(p mod 6)^e.

Original entry on oeis.org

1, 3, 5, 9, 11, 15, 2, 27, 25, 33, 11, 45, 2, 6, 55, 81, 11, 75, 2, 99, 10, 33, 11, 135, 121, 6, 125, 18, 11, 165, 2, 243, 55, 33, 22, 225, 2, 6, 10, 297, 11, 30, 2, 99, 275, 33, 11, 405, 4, 363, 55, 18, 11, 375, 121, 54, 10, 33, 11, 495, 2, 6, 50, 729, 22, 165, 2, 99, 55, 66, 11, 675, 2, 6, 605, 18, 22, 30, 2, 891, 625, 33, 11, 90, 121, 6

Offset: 1

Antti Karttunen, Oct 06 2018

For all i, j:

A319716(i) = A319716(j) => a(i) = a(j) => A319690(i) = A319690(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. A319690, A319716, A319984, A319985, A319987, A320116, A320117.

A319986(n) = { my(f=factor(n)); prod(i=1, #f~, (prime(f[i, 1]%6))^f[i, 2]); };

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)).

cp's OEIS Frontend

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

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A319985 Fully multiplicative with a(p^e) = prime(p mod 12)^e.

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A319986 Fully multiplicative with a(p^e) = prime(p mod 6)^e.

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

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