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.

A068357 Duplicate of A067891.

Original entry on oeis.org

367, 919, 30593, 95393, 117571, 124759, 147341, 197261, 334541, 344417, 463219
Offset: 1

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Keywords

A067889 Primes sandwiched between two numbers having same number of divisors.

Original entry on oeis.org

7, 19, 41, 103, 137, 199, 307, 349, 491, 739, 823, 919, 1013, 1061, 1193, 1277, 1289, 1409, 1433, 1447, 1481, 1543, 1609, 1667, 1721, 1747, 2153, 2357, 2441, 2617, 2683, 2777, 3259, 3319, 3463, 3581, 3593, 3769, 3797, 3911, 3943, 4013, 4217, 4423, 4457
Offset: 1

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Author

Benoit Cloitre, Mar 02 2002

Keywords

Comments

Primes p such that tau(p+1) = tau(p-1) where tau(k) = A000005(k).
These are the primes in sequence A067888 of numbers n such that tau(n+1) = tau(n-1). - M. F. Hasler, Aug 06 2015

Examples

			7 is a member as 6 and 8 both have 4 divisors; 19 is a member as 18 and 20 both have 6 divisors each.
		

Crossrefs

Cf. A067888, A067891 (analog with sigma).

Programs

  • Maple
    with(numtheory):j := 0:for i from 1 to 10000 do b := ithprime(i): if nops(divisors(b-1))=nops(divisors(b+1)) then j := j+1:a[j] := b:fi:od:seq(a[k],k=1..j);
  • Mathematica
    Prime[ Select[ Range[ 700 ], Length[ Divisors[ Prime[ #1 ] - 1 ]] == Length[ Divisors[ Prime[ #1 ] + 1 ]] & ]]
    Select[Prime[Range[1000]],DivisorSigma[0,#-1]==DivisorSigma[0,#+1]&] (* Harvey P. Dale, Jun 08 2018 *)
  • PARI
    is_A067889(p)=numdiv(p-1)==numdiv(p+1)&&isprime(p) \\ M. F. Hasler, Jul 31 2015

Formula

a(n) seems curiously to be asymptotic to 25*n*log(n). [From the number of terms up to 10^8, 10^9, 10^10 and 10^11, i.e., 306147, 2616930, 22835324 and 202105198, this constant can be estimated by 25.858..., 25.858..., 25.845... and 25.872..., respectively. - Amiram Eldar, Jun 28 2022]

A169595 Primes p such that sigma(p+2)=sigma(p-2).

Original entry on oeis.org

53, 20543, 47843, 176227, 396953, 471187, 995887, 1083113, 1867253, 5022653, 17449567, 22873583, 32003407, 38673847, 59808803, 96144127, 113561243, 143570873, 164563687, 225835807, 238818893, 272773499, 286557983, 349504957
Offset: 1

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Keywords

Crossrefs

Cf. A067891.
Subsequence of A223091.

Programs

  • Mathematica
    f[n_]:=Plus@@Divisors[Prime[n]-2]==Plus@@Divisors[Prime[n]+2]; lst={};Do[If[f[n],AppendTo[lst,Prime[n]]],{n,2*9!}];lst

Extensions

a(11)-a(24) from Donovan Johnson, Dec 08 2009
a(25)-a(200) from Martin Møller Skarbiniks Pedersen, May 31 2016

A169596 Primes p such that sigma(p+3) = sigma(p-3).

Original entry on oeis.org

23, 653, 947, 2027, 4133, 5431, 18433, 30089, 39733, 61667, 71233, 120947, 148439, 163673, 238801, 265813, 493853, 502499, 1070033, 1100921, 1139141, 1176127, 1207447, 1364401, 1959961, 1979281, 2164471, 3156319, 3175967, 3195233
Offset: 1

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Keywords

Crossrefs

Programs

  • Mathematica
    Select[Prime@ Range[10^5], Equal @@ DivisorSigma[1, # + {-3, 3}] &] (* Giovanni Resta, May 15 2016 *)
Showing 1-4 of 4 results.