A103664 -id:A103664 - cp's OEIS frontend

A103665 Primes p such that the number of divisors of p-1 is greater than the number of divisors of p+1.

13, 31, 37, 43, 61, 67, 73, 97, 101, 109, 113, 127, 151, 157, 163, 181, 193, 211, 229, 241, 257, 271, 277, 281, 283, 313, 331, 337, 353, 373, 379, 397, 401, 409, 421, 433, 457, 463, 487, 521, 523, 541, 547, 571, 577, 601, 613, 617, 631, 641, 661, 673, 677

Offset: 1

Hugo Pfoertner, Feb 19 2005

nonn

Mathematica coding by Wouter Meeussen and Robert G. Wilson v.

			a(1)=13 because d(12)=6 > d(14)=4.

Hugo Pfoertner, Table of n, a(n) for n = 1..10000

Cf. A008328 number of divisors of p-1, A008329 number of divisors of p+1, A103664, A103666, A103667.

Select[Prime[Range[2, 140]], Length[Divisors[ # - 1]] > Length[Divisors[ # + 1]] &]
Select[Prime[Range[200]],DivisorSigma[0,#-1]>DivisorSigma[0,#+1]&] (* Harvey P. Dale, Aug 21 2022 *)

forprime (k=2,700,if(numdiv(k-1)>numdiv(k+1),print1(k,", ")))
\\ Hugo Pfoertner, Nov 30 2017

A145337 a(n) = d(p(n)+1) - d(p(n)-1), where d(m) = the number of divisors of m, p(n) = the n-th prime.

Original entry on oeis.org

1, 1, 1, 0, 2, -2, 1, 0, 4, 2, -2, -5, 0, -2, 6, 2, 8, -8, -2, 4, -8, 2, 8, 4, -6, -1, 0, 8, -4, -2, -4, 4, 0, 4, 6, -4, -8, -4, 12, 2, 14, -10, 6, -10, 3, 0, -10, 4, 8, -4, 4, 12, -14, 10, -1, 12, 10, -6, -8, -8, -2, 6, 0, 8, -12, 2, -10, -14, 8, 0, -4, 20, 2, -4, -4, 12, 10, -14, -7, -8

Offset: 0

Leroy Quet, Oct 08 2008

sign

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Cf. A008328, A008329, A067889, A103664, A103665, A145338.

A000005 := proc(n) numtheory[tau](n) ; end:
A008328 := proc(n) A000005(ithprime(n)-1) ; end:
A008329 := proc(n) A000005(ithprime(n)+1) ; end:
A145337 := proc(n) A008329(n)-A008328(n) ; end: # R. J. Mathar, Oct 10 2008

DivisorSigma[0,#+1]-DivisorSigma[0,#-1]&/@Prime[Range[80]] (* Harvey P. Dale, Nov 01 2011 *)

a(n) = A008329(n) - A008328(n). - R. J. Mathar, Oct 10 2008

More terms from R. J. Mathar and Ray Chandler, Oct 10 2008

A145339 a(n) = the minimum of d(p(n)-1) and d(p(n)+1), where d(m) is the number of divisors of m and p(n) is the n-th prime.

Original entry on oeis.org

1, 2, 3, 4, 4, 4, 5, 6, 4, 6, 6, 4, 8, 6, 4, 6, 4, 4, 6, 8, 4, 8, 4, 8, 6, 8, 8, 4, 8, 8, 8, 8, 8, 8, 6, 8, 4, 6, 4, 6, 4, 8, 8, 4, 9, 12, 6, 8, 4, 8, 8, 8, 6, 8, 8, 4, 6, 10, 4, 8, 6, 6, 12, 8, 4, 6, 6, 6, 4, 12, 8, 4, 8, 8, 12, 4, 6, 4, 8, 8, 8, 4, 8, 8, 8, 8, 14, 4, 12, 10, 4, 4, 8, 12, 8, 4, 6, 12, 6, 4, 6

Offset: 1

Leroy Quet, Oct 08 2008

nonn

Cf. A145340, A008328, A008329, A067889, A103664, A103665.

Table[Min[DivisorSigma[0, Prime[n]-1], DivisorSigma[0, Prime[n]+1]], {n, 1, 100}] (* Stefan Steinerberger, Oct 11 2008 *)

a(n) = my(p = prime(n)); min(numdiv(p-1), numdiv(p+1)); \\ Michel Marcus, Sep 28 2018

More terms from Stefan Steinerberger and Ray Chandler, Oct 11 2008

A103886 Rearrangement of prime numbers p according to number of divisors of p-/+1.

Original entry on oeis.org

2, 7, 13, 3, 19, 31, 5, 41, 37, 11, 103, 43, 17, 137, 61, 23, 199, 67, 29, 307, 73, 47, 349, 97, 53, 491, 101, 59, 739, 109

Offset: 1

Zak Seidov, Feb 20 2005

nonn

Number of divisors of p-1 (less than, equals and larger than) number of divisors of p+1. A103887 - position of p(n) in the sequence.

Cf. A067889, A103664, A103665, A103887.

Table[{A103664[[n]], A067889[[n]], A103665[[n]]}, {n, 10}]//Flatten

a(3k-2)=A103664(k); a(3k-1)=A067889(k); a(3k)=A103665(k); (k=1, 2, ...)

A103887 Position of p(n) in rearrangement of prime numbers A103886.

Original entry on oeis.org

1, 4, 7, 2, 10, 3, 13, 5, 16, 19, 6, 9, 8, 12, 22, 25, 28, 15, 18

Offset: 1

Zak Seidov, Feb 20 2005

nonn

Cf. A067889, A103664, A103665, A103886.

Table[Position[A103886, Prime[n]], {n, 19}]//Flatten

A145340 a(n) = the maximum of d(p(n)-1) and d(p(n)+1), where d(m) is the number of divisors of m and p(n) is the n-th prime.

Original entry on oeis.org

2, 3, 4, 4, 6, 6, 6, 6, 8, 8, 8, 9, 8, 8, 10, 8, 12, 12, 8, 12, 12, 10, 12, 12, 12, 9, 8, 12, 12, 10, 12, 12, 8, 12, 12, 12, 12, 10, 16, 8, 18, 18, 14, 14, 12, 12, 16, 12, 12, 12, 12, 20, 20, 18, 9, 16, 16, 16, 12, 16, 8, 12, 12, 16, 16, 8, 16, 20, 12, 12, 12, 24, 10, 12, 16, 16, 16

Offset: 1

Leroy Quet, Oct 08 2008

nonn

Cf. A145339, A008328, A008329, A067889, A103664, A103665.

Table[Max[DivisorSigma[0, Prime[n]-1], DivisorSigma[0, Prime[n]+1]], {n, 1, 100}] (* Stefan Steinerberger, Oct 11 2008 *)

More terms from Stefan Steinerberger and Ray Chandler, Oct 11 2008

cp's OEIS Frontend

A103665 Primes p such that the number of divisors of p-1 is greater than the number of divisors of p+1.

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A145337 a(n) = d(p(n)+1) - d(p(n)-1), where d(m) = the number of divisors of m, p(n) = the n-th prime.

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A145339 a(n) = the minimum of d(p(n)-1) and d(p(n)+1), where d(m) is the number of divisors of m and p(n) is the n-th prime.

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A103886 Rearrangement of prime numbers p according to number of divisors of p-/+1.

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A103887 Position of p(n) in rearrangement of prime numbers A103886.

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A145340 a(n) = the maximum of d(p(n)-1) and d(p(n)+1), where d(m) is the number of divisors of m and p(n) is the n-th prime.

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