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 1-3 of 3 results.

A067532 Numbers k such that k + number of divisors of k is a prime.

Original entry on oeis.org

1, 3, 4, 5, 11, 15, 17, 27, 29, 33, 39, 41, 55, 57, 59, 64, 69, 71, 85, 93, 100, 101, 105, 107, 123, 133, 137, 145, 149, 159, 165, 175, 177, 179, 187, 189, 191, 197, 219, 227, 231, 235, 237, 239, 245, 247, 253, 255, 259, 265, 267, 269, 273, 275, 281, 285, 303
Offset: 1

Views

Author

Amarnath Murthy, Feb 17 2002

Keywords

Comments

Smaller of the twin primes (A001359) is a term.

Examples

			a(1) = 1 (1+d(1) = 1+1 = 2 = prime).
a(2) = 3 (3+d(3) = 3+2 = 5 = prime).

Links

Crossrefs

Cf. A000005, A001359, A067531.

Programs

  • Maple
    with(numtheory): for n from 3 to 500 do if isprime(n+tau(n)) then printf(`%d,`,n) fi:od: # James Sellers, Feb 18 2002
  • Mathematica
    a067532[n_] := Select[Range[n], PrimeQ[# + DivisorSigma[0, #]] &]; a067532[303] (* Michael De Vlieger, Dec 22 2014 *)
  • PARI
    isok(k) = isprime(k + numdiv(k)); \\ Amiram Eldar, Jan 27 2025

Extensions

More terms from James Sellers, Feb 18 2002
Sequence corrected by Juri-Stepan Gerasimov, Oct 18 2009
Offset corrected by N. J. A. Sloane, Oct 21 2009
Corrected by Charles R Greathouse IV, Mar 19 2010

A067533 Numbers k such that both k - tau(k) and k + tau(k) are prime where tau(k) = A000005(k).

Original entry on oeis.org

5, 15, 27, 33, 57, 93, 105, 165, 177, 189, 231, 237, 245, 267, 275, 285, 345, 375, 393, 425, 453, 555, 567, 573, 597, 609, 637, 651, 687, 723, 833, 933, 1005, 1025, 1095, 1167, 1209, 1221, 1227, 1293, 1311, 1431, 1445, 1479, 1491, 1527, 1551, 1563, 1573
Offset: 1

Views

Author

Amarnath Murthy, Feb 17 2002

Keywords

Examples

			57 is a term as tau(57) = 4 and 57-4 = 53 and 57+4 = 61 are both primes.

Links

Crossrefs

Intersection of A067531 and A067532.

Programs

  • Mathematica
    Select[Range[2000],With[{t=DivisorSigma[0,#]},AllTrue[#+{t,-t},PrimeQ]&]]  (* Harvey P. Dale, Mar 16 2025 *)
  • PARI
    isok(n) = my(nd = numdiv(n)); isprime(n-nd) && isprime(n+nd); \\ Michel Marcus, Oct 12 2018

Extensions

More terms from Sascha Kurz, Mar 19 2002
Offset corrected by Alois P. Heinz, Oct 10 2018
Name changed by David A. Corneth, Oct 12 2018

A158338 Composite numbers k such that k - number of divisors of k = prime.

Original entry on oeis.org

6, 15, 16, 21, 27, 33, 35, 51, 57, 65, 77, 87, 93, 105, 111, 135, 141, 143, 155, 161, 165, 177, 183, 185, 189, 201, 203, 215, 231, 237, 245, 267, 275, 285, 287, 321, 335, 341, 345, 357, 371, 375, 377, 393, 413, 425, 429, 437, 447, 453, 465, 471
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Mar 16 2009, Nov 14 2009

Keywords

Comments

Subsequence of A067531. - Michel Marcus, Dec 22 2014

Examples

			6 is composite and has 4 divisors (1, 2, 3, 6); 6 - 4 = 2, which is prime, so 6 is in the sequence.
15 is composite and has 4 divisors (1, 3, 5, 15); 15 - 4 = 11, which is prime, so 15 is in the sequence.
16 is composite and has 5 divisors (1, 2, 4, 8, 16); 16 - 5 = 11, which is prime, so 16 is in the sequence.

Links

Crossrefs

Cf. A000005, A000040, A002808, A035004, A067531.

Programs

  • Magma
    [k:k in [1..500]|not IsPrime(k) and IsPrime(k-#Divisors(k))]; // Marius A. Burtea, Jul 16 2019
  • Mathematica
    Select[Range[500], CompositeQ[#] && PrimeQ[# - DivisorSigma[0, #]] &] (* Amiram Eldar, Jul 16 2019 *)

Extensions

Extended by R. J. Mathar, May 19 2010
Showing 1-3 of 3 results.

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

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