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.

Previous Showing 11-15 of 15 results.

A366656 Number of divisors of 8^n+1.

Original entry on oeis.org

2, 3, 4, 8, 4, 12, 16, 12, 8, 20, 48, 24, 16, 12, 64, 64, 8, 48, 64, 24, 16, 64, 64, 24, 32, 96, 768, 192, 32, 24, 1536, 24, 8, 256, 512, 1536, 64, 96, 256, 64, 64, 96, 1024, 48, 128, 1280, 256, 96, 128, 96, 8192, 1024, 32, 48, 1024, 2304, 256, 192, 256, 192
Offset: 0

Views

Author

Sean A. Irvine, Oct 15 2023

Keywords

Examples

			a(4)=4 because 8^4+1 has divisors {1, 17, 241, 4097}.

Links

Crossrefs

Cf. A062395, A000005, A057936, A274905, A366653, A366638, A366655, A366657, A366658.
Cf. A046798, A366577, A366606, A366616, A366628, A366637, A366665, A344897, A366688, A366714.

Programs

  • Maple
    a:=n->numtheory[tau](8^n+1):
seq(a(n), n=0..100);
  • Mathematica
    DivisorSigma[0, 8^Range[0,59] + 1] (* Paul F. Marrero Romero, Nov 12 2023 *)
  • PARI
    a(n) = numdiv(8^n+1);

Formula

a(n) = sigma0(8^n+1) = A000005(A062395(n)).
a(n) = A046798(3*n). - Max Alekseyev, Jan 09 2024

A366657 Sum of the divisors of 8^n+1.

Original entry on oeis.org

3, 13, 84, 800, 4356, 51792, 351120, 3100240, 17041416, 211053040, 1494039792, 12611914848, 73234343952, 794382536272, 5936210280000, 60037292774400, 282937726148616, 3264911394064320, 24128875076496960, 208532141890460960, 1225825603154905104
Offset: 0

Views

Author

Sean A. Irvine, Oct 15 2023

Keywords

Examples

			a(4)=4356 because 8^4+1 has divisors {1, 17, 241, 4097}.

Links

Crossrefs

Cf. A062395, A000203, A057936, A274905, A366653, A366655, A366656, A366658.
Cf. A069061, A366578, A366607, A366617, A366629, A366638, A366666, A366668, A366689, A366715.

Programs

  • Maple
    a:=n->numtheory[sigma](8^n+1):
seq(a(n), n=0..100);
  • Mathematica
    DivisorSigma[1, 8^Range[0,20]+1] (* Paul F. Marrero Romero, Nov 19 2023 *)

Formula

a(n) = sigma(8^n+1) = A000203(A062395(n)).
a(n) = A069061(3*n). - Max Alekseyev, Jan 09 2024

A366713 Number of prime factors of 12^n + 1 (counted with multiplicity).

Original entry on oeis.org

1, 1, 2, 3, 2, 2, 3, 3, 3, 5, 4, 2, 4, 5, 4, 7, 2, 3, 5, 4, 6, 9, 6, 4, 6, 6, 5, 10, 3, 3, 6, 3, 2, 9, 4, 5, 7, 4, 5, 11, 4, 5, 6, 5, 4, 12, 3, 5, 5, 5, 10, 9, 5, 5, 10, 7, 9, 11, 8, 6, 10, 5, 6, 15, 5, 9, 11, 4, 5, 12, 10, 3, 10, 5, 8, 17, 5, 6, 9, 4, 6, 15
Offset: 0

Views

Author

Sean A. Irvine, Oct 17 2023

Keywords

Links

Crossrefs

Cf. A178248, A001222, A054992, A057934, A057935, A057936, A057937, A057938, A057939, A057940, A057941, A366712, A366714, A366715, A366716, A366719, A366720, A366708, A366687.

Programs

  • Mathematica
    PrimeOmega[12^Range[70]+1]
  • PARI
    a(n)=bigomega(12^n+1)

Formula

a(n) = bigomega(12^n+1) = A001222(A178248(n)).

A366687 Number of prime factors of 11^n + 1 (counted with multiplicity).

Original entry on oeis.org

1, 3, 2, 5, 2, 4, 4, 4, 3, 7, 3, 7, 4, 6, 5, 8, 3, 6, 5, 7, 4, 7, 4, 7, 7, 6, 3, 10, 6, 6, 6, 7, 4, 13, 6, 11, 7, 5, 4, 11, 5, 6, 9, 5, 6, 13, 6, 7, 5, 8, 6, 11, 3, 7, 9, 13, 7, 12, 6, 7, 8, 6, 4, 13, 3, 10, 8, 9, 7, 14, 8, 6, 10, 8, 8, 13, 6, 12, 12, 7, 10
Offset: 0

Views

Author

Sean A. Irvine, Oct 16 2023

Keywords

Links

Crossrefs

Cf. A034524, A001222, A057934, A062308, A366686, A366688, A366689, A366690.
Cf. A054992, A057941, A057940, A057939, A057938, A057937, A057936, A057935, A057934, A366713.

Programs

  • Mathematica
    PrimeOmega[11^Range[70]+1]
  • PARI
    a(n)=bigomega(11^n+1)

Formula

a(n) = bigomega(11^n+1) = A001222(A034524(n)).

A068150 First of n consecutive primes == 7 mod 10.

Original entry on oeis.org

7, 337, 1627, 57427, 192637, 776257, 15328637, 70275277, 244650317, 452942827, 452942827, 73712513057, 319931193737, 2618698284817, 10993283241587, 54010894438097, 101684513099627, 196948379177587
Offset: 1

Views

Author

Amarnath Murthy, Feb 24 2002

Keywords

Comments

The next set of consecutive primes includes numbers > 10000000. - Larry Reeves (larryr(AT)acm.org), Jun 14 2002
Same as A057626 except a(1). - Jens Kruse Andersen, Jun 03 2006

Examples

			a(3) = 1627 as it is the start of the first occurrence of the three consecutive prime 1627, 1637 and 1657 ending in 7.

Links

Crossrefs

Cf. A057618, A057631, A057936, A054681.

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Jun 14 2002
More terms from Labos Elemer, Jun 16 2003
More terms from Enoch Haga, Jan 17 2004. a(12) is from Phil Carmody.
More terms from Jens Kruse Andersen, Jun 03 2006
a(15)-a(18) from Giovanni Resta, Aug 04 2013
Previous Showing 11-15 of 15 results.

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

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