A319823 - OEIS

A319823

Primes p such that min(d(p-1), d(p+1)) is larger than the corresponding values of all previous primes, where d(n) is the number of divisors of n (A000005).

2, 3, 5, 7, 17, 19, 41, 197, 199, 449, 701, 881, 3079, 4159, 18089, 40699, 51679, 90271, 388961, 403649, 446081, 906751, 1276001, 12227489, 37487449, 53308529, 59522849, 109245401, 285258401, 459712639, 1381951999, 2560742911, 2969200961, 8505402751

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OFFSET

1,1

COMMENTS

Problem 104 in Sierpinski's book is to prove that this sequence is infinite.

The corresponding values of min(d(p-1), d(p+1)) are 1, 2, 3, 4, 5, 6, 8, 9, 12, 14, 16, 18, 20, 28, 32, 36, 40, 48, 50, 56, 64, 80, 96, 128, 144, 160, 168, 192, 216, 256, 288, 320, 336, 384, ...

REFERENCES

W. Sierpinski, 250 Problems in Elementary Number Theory, New York: American Elsevier, 1970, problem #104, pp. 9, 58-59.

LINKS

Table of n, a(n) for n=1..34.

MATHEMATICA

s={}; f[p_] := Min[DivisorSigma[0, p-1], DivisorSigma[0, p+1]]; p=2; fm=0; Do[f1 = f[p]; If[f1>fm, AppendTo[s, p]; fm=f1]; p=NextPrime[p], {k, 1, 100}]; s

PROG

(PARI) f(p)=min(numdiv(p-1), numdiv(p+1));

fm=0; forprime(p=1, 1000, f1=f(p); if(f1>fm, print1(p, ", "); fm=f1))

CROSSREFS

Cf. A000005, A000040, A145339.

Sequence in context: A127049 A142885 A108547 * A286499 A116947 A066277

Adjacent sequences: A319820 A319821 A319822 * A319824 A319825 A319826

KEYWORD

nonn

AUTHOR

Amiram Eldar, Sep 28 2018

STATUS

approved