cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A093034 Primes of the form 1 + multiple perfect number.

Original entry on oeis.org

2, 7, 29, 673, 30241, 523777, 2178541, 23569921, 33550337, 66433720321, 137438691329, 30823866178561, 796928461056001, 1802582780370364661761, 9186050031556349952001, 2827987212986831882236723201, 630532357710420079508428362350593, 1928622300236318049928258133164033
Offset: 1

Views

Author

Labos Elemer, May 12 2004

Keywords

Comments

From M. F. Hasler and Farideh Firoozbakht, Apr 08 2010: (Start)
Theorem: If p is a term of this sequence and p-1 is a t-perfect number then for each positive integer k, x=p^k is a solution to the equation sigma(phi(x)) = t*(x-1).
Proof: sigma(phi(x)) = sigma(phi(p^k)) = sigma((p-1)*p^(k-1)) = sigma(p-1)*sigma(p^(k-1)) = t*(p-1)*(p^k-1)/(p-1) = t*(p^k-1) = t*(x-1). (End)

Links

Crossrefs

Cf. A000010 (phi), A000203 (sigma), A007691, A171263, A171264, A171265.

Extensions

a(11)-a(16) from Donovan Johnson, Nov 30 2008
a(17)-a(18) from Amiram Eldar, May 09 2024

A171263 Primes of the form 1 + 4-multiperfect numbers.

Original entry on oeis.org

30241, 2178541, 23569921, 66433720321, 630532357710420079508428362350593, 1928622300236318049928258133164033, 651350717502447739281012140234441171379683329
Offset: 1

Views

Author

M. F. Hasler and Farideh Firoozbakht, Apr 15 2010

Keywords

Comments

A subsequence of A093034. If p is a term of this sequence then for each positive integer k, x=p^k is a solution for the equation sigma(phi(x))=4(x-1). See comment lines of the sequence A093034.

Examples

			p=30241 is prime and sigma(p-1)/(p-1)=4, so p is in the sequence.

Crossrefs

Cf. A027687, A093034, A171264, A171265.

A171264 Primes of the form 1 + 5-multiperfect numbers.

Original entry on oeis.org

30823866178561, 796928461056001, 1802582780370364661761, 2827987212986831882236723201, 68688966922031309945174465761834751373920047004215278394826366933532673
Offset: 1

Views

Author

M. F. Hasler and Farideh Firoozbakht, Apr 15 2010

Keywords

Comments

A subsequence of A093034. If p is a term of this sequence then for each positive integer k, x=p^k is a solution for the equation sigma(phi(x))=5(x-1). See comment lines of the sequence A093034.

Examples

			p=30823866178561 is prime and sigma(p-1)/(p-1)=5, so p is in the sequence.

Crossrefs

Cf. A027687, A093034, A171263, A171265.

A171266 Primes of the form 1 + triperfect numbers.

Original entry on oeis.org

673, 523777
Offset: 1

Views

Author

M. F. Hasler and Farideh Firoozbakht, Apr 15 2010

Keywords

Comments

A subsequence of A093034.
If p is a term of this sequence then for each positive integer k, x=p^k
is a solution for the equation sigma(phi(x))=3(x-1). See comment lines of
the sequence A093034.

Examples

			p=673 is prime and sigma(p-1)/(p-1)=3, so p is in the sequence.

Links

Crossrefs

Cf. A005820, A093034, A171263, A171264, A171265.
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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