A071630 -id:A071630 - cp's OEIS frontend

A071629 Number of terms in the set InvPhi(4*prime(n)), where prime(n) is the n-th prime.

5, 6, 5, 2, 3, 2, 0, 0, 3, 3, 0, 2, 3, 2, 0, 3, 0, 0, 2, 0, 2, 2, 3, 3, 2, 0, 0, 0, 0, 3, 2, 3, 0, 2, 0, 0, 0, 2, 0, 3, 3, 0, 3, 2, 0, 2, 0, 0, 0, 0, 3, 3, 0, 3, 0, 0, 0, 0, 2, 3, 0, 3, 2, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 2, 0, 0, 0, 0, 0, 2, 3, 0, 3, 2, 0, 3, 0, 0, 0, 0, 0, 0, 2, 3, 2, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 1

Labos Elemer, May 30 2002

nonn

			For n=5: invphi(4*11) = [69,92,138], a(5) = 3.

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Donovan Johnson)
Max Alekseyev, PARI/GP Scripts for Miscellaneous Math Problems (invphi.gp).

Cf. A000010, A002202, A005277, A007617, A058888, A071630-A071634.

[seq(nops(invphi(4*ithprime(i))),i=1..128)];

a(n) = invphiNum(4*prime(n)); \\ Amiram Eldar, Nov 07 2024, using Max Alekseyev's invphi.gp

A071634 Number of terms in the set InvPhi(1048576*prime(n)), where prime(n) is the n-th prime.

Original entry on oeis.org

23, 112, 81, 64, 75, 48, 36, 28, 43, 68, 14, 80, 35, 50, 0, 43, 28, 28, 46, 52, 44, 32, 38, 49, 48, 37, 10, 34, 24, 47, 34, 65, 19, 28, 59, 20, 32, 82, 15, 30, 61, 32, 48, 62, 10, 32, 2, 26, 18, 16, 65, 77, 0, 46, 8, 0, 43, 18, 56, 60, 0, 38, 40, 13, 36, 26, 44, 46, 41, 12, 0

Offset: 1

Labos Elemer, May 30 2002

nonn

			InvPhi(1048576*211) = {221249537,442499074}, a(47) = 2.
Observe that a(15) = 0 because 47 needs a very large 2^i multiplier (instead of 1048576) to give a nonempty InvPhi set.

Donovan Johnson, Table of n, a(n) for n = 1..1000
Max Alekseyev, PARI/GP Scripts for Miscellaneous Math Problems (invphi.gp).

Cf. A000010, A002202, A005277, A007617, A058888, A071629, A071630, A071631, A071632, A071633.

>[seq(nops(invphi(1048576*ithprime(i))),i=1..128)];

a(n) = invphiNum(1048576 * prime(n)); \\ Amiram Eldar, Nov 11 2024, using Max Alekseyev's invphi.gp

A071632 Number of terms in the set InvPhi(1024*prime(n)), where prime(n) is the n-th prime.

Original entry on oeis.org

13, 43, 31, 24, 32, 16, 13, 8, 14, 27, 4, 24, 11, 16, 0, 18, 7, 8, 16, 19, 16, 12, 18, 19, 18, 12, 0, 14, 6, 18, 10, 23, 9, 10, 17, 8, 4, 28, 5, 11, 20, 12, 18, 22, 0, 10, 0, 6, 0, 6, 21, 32, 0, 11, 4, 0, 16, 8, 20, 19, 0, 18, 14, 3, 10, 5, 12, 16, 14, 2, 0, 26, 0, 16, 0, 0, 0, 14, 14

Offset: 1

Labos Elemer, May 30 2002

nonn

			InvPhi(1024*31) = {39685,63496,79370,95244}, so a(11) = 4.
Observe that a(15) = 0 because 47 needs a very large 2^i multiplier (instead of 1024) to give a nonempty InvPhi set.

Donovan Johnson, Table of n, a(n) for n = 1..1000
Max Alekseyev, PARI/GP Scripts for Miscellaneous Math Problems (invphi.gp).

Cf. A000010, A002202, A005277, A007617, A058888, A071629, A071630, A071631, A071633, A071634.

[seq(nops(invphi(1024*ithprime(i))),i=1..128)];

a(n) = invphiNum(1024 * prime(n)); \\ Amiram Eldar, Nov 11 2024, using Max Alekseyev's invphi.gp

A071633 Number of terms in the set InvPhi(65536*prime(n)), where prime(n) is the n-th prime.

Original entry on oeis.org

19, 82, 59, 46, 56, 34, 26, 20, 31, 52, 10, 56, 24, 34, 0, 30, 20, 20, 32, 37, 32, 24, 30, 37, 34, 24, 2, 26, 16, 35, 22, 46, 15, 20, 38, 14, 20, 58, 11, 22, 42, 24, 33, 46, 3, 20, 0, 18, 10, 12, 44, 56, 0, 29, 8, 0, 31, 14, 38, 44, 0, 30, 28, 9, 24, 18, 30, 34, 29, 8, 0, 50, 6

Offset: 1

Labos Elemer, May 30 2002

nonn

			invphi(65536*103) = {6750209,13500418}, so a(27) = 2.
Observe that a(15) = 0 because 47 needs very large 2^i multiplier (instead of 65536) to give nonempty InvPhi set.

Donovan Johnson, Table of n, a(n) for n = 1..1000
Max Alekseyev, PARI/GP Scripts for Miscellaneous Math Problems (invphi.gp).

Cf. A000010, A005277, A007617, A058888, A002202, A071629, A071630, A071631, A071632, A071634.

[seq(nops(invphi(65536*ithprime(i))),i=1..128)];

a(n) = invphiNum(65536 * prime(n)); \\ Amiram Eldar, Nov 11 2024, using Max Alekseyev's invphi.gp

cp's OEIS Frontend

A071629 Number of terms in the set InvPhi(4*prime(n)), where prime(n) is the n-th prime.

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A071634 Number of terms in the set InvPhi(1048576*prime(n)), where prime(n) is the n-th prime.

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Maple

PARI

A071632 Number of terms in the set InvPhi(1024*prime(n)), where prime(n) is the n-th prime.

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Maple

PARI

A071633 Number of terms in the set InvPhi(65536*prime(n)), where prime(n) is the n-th prime.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Maple

PARI