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.

A090483 Indices of zero in A090482.

Original entry on oeis.org

1, 2, 4, 6, 9, 15, 19
Offset: 1

Views

Author

Amarnath Murthy, Dec 02 2003

Keywords

Comments

I conjecture there are no more terms; I've checked up to 200. - David Wasserman, Nov 17 2005

Crossrefs

Cf. A090481, A090482.

Extensions

Two more terms from David Wasserman, Nov 17 2005

A090481 Primes p such that tau(p-1)+tau(p+1) is larger than for any previous term. (Smallest prime sandwiched between more composite numbers.)

Original entry on oeis.org

2, 3, 5, 7, 11, 17, 19, 29, 41, 71, 179, 181, 239, 419, 701, 839, 881, 1259, 1871, 2161, 2521, 4159, 5039, 7561, 10079, 13441, 13859, 20161, 22679, 30241, 35281, 45361, 55439, 65519, 110879, 138599, 151201, 166319, 226799, 262079, 327599, 332641
Offset: 1

Views

Author

Amarnath Murthy, Dec 02 2003

Keywords

Examples

			17 follows 11 and 13 is not a term as tau(10) + tau(12) = tau(12) + tau(14) = 10.

Links

Crossrefs

Cf. A090482, A000005.

Programs

  • Mathematica
    a = {}; t = 0; Do[p = Prime[n]; s = DivisorSigma[0, p - 1] + DivisorSigma[0, p + 1]; If[s > t, t = s; AppendTo[a, p]], {n, 1, 10^5}]; a (* Robert G. Wilson v, Dec 04 2003 *)

Extensions

More terms from Robert G. Wilson v, Dec 04 2003

A175144 a(n) = d(p(n)-1) + d(p(n)+1), where p(n) is the n-th prime, and where d(m) is the number of divisors of m.

Original entry on oeis.org

3, 5, 7, 8, 10, 10, 11, 12, 12, 14, 14, 13, 16, 14, 14, 14, 16, 16, 14, 20, 16, 18, 16, 20, 18, 17, 16, 16, 20, 18, 20, 20, 16, 20, 18, 20, 16, 16, 20, 14, 22, 26, 22, 18, 21, 24, 22, 20, 16, 20, 20, 28, 26, 26, 17, 20, 22, 26, 16, 24, 14, 18, 24, 24, 20, 14, 22, 26, 16, 24, 20
Offset: 1

Views

Author

Leroy Quet, Feb 24 2010

Keywords

Comments

If a(n) is a record, then the n-th prime is in sequence A090481.

Links

Crossrefs

Cf. A000005, A006093, A008864, A090481, A090482, A175146.

Programs

  • Maple
    taudiff := proc(n) numtheory[tau](n-1)+numtheory[tau](n+1) ; end proc: A175144 := proc(n) taudiff(ithprime(n)) ; end proc: seq(A175144(n),n=1..80) ; # R. J. Mathar, Mar 03 2010
  • Mathematica
    Table[p = Prime[n]; DivisorSigma[0, p - 1] + DivisorSigma[0, p + 1], {n, 100}]
Total[DivisorSigma[0,{#-1,#+1}]]&/@Prime[Range[80]] (* Harvey P. Dale, Feb 25 2012 *)
  • PARI
    a(n) = numdiv(prime(n)-1) + numdiv(prime(n)+1); \\ Amiram Eldar, Apr 17 2024
  • PARI
    lista(pmax) = forprime(p = 1, pmax, print1(numdiv(p-1) + numdiv(p+1), ", ")); \\ Amiram Eldar, Apr 17 2024

Formula

a(n) = A000005(A006093(n)) + A000005(A008864(n)). - R. J. Mathar, Mar 03 2010

Extensions

More terms from R. J. Mathar, Mar 03 2010

A189536 The smallest prime p such that tau(p-1) + tau(p+1) = prime(n), or 0 if no such prime exists; where tau(k) is the number of divisors of k.

Original entry on oeis.org

0, 2, 3, 5, 17, 37, 101, 0, 401, 3137, 4357, 62501, 21317, 16901, 1008017, 15877, 1020101, 33857, 69697, 14401, 331777, 78401, 32401, 57601, 828101, 40195601, 32080897, 3326977, 876097, 476101, 199374401, 4326401, 14440001, 1299601, 33918977, 3459601, 2647719937, 145540097
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Apr 23 2011

Keywords

Comments

This is sequence A090482(n) for prime n.

Crossrefs

Cf. A000005, A000668, A002496, A090482, A175144 (tau(p-1)+tau(p+1)).

Programs

  • Mathematica
    nn = 25; t = Table[-1, {nn}]; t[[1]] = 0; t[[8]] = 0; cnt = 2; p = 1; While[cnt < nn, p = NextPrime[p]; s = DivisorSigma[0, p - 1] + DivisorSigma[0, p + 1]; If[PrimeQ[s], i = PrimePi[s]; If[i <= nn && t[[i]] == -1, t[[i]] = p; cnt++]]]; t (* T. D. Noe, Apr 28 2011 *)

Extensions

a(26)-a(38) from Amiram Eldar, Jan 25 2025
Showing 1-4 of 4 results.

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