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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).
0
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
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.
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
KEYWORD
nonn
AUTHOR
Amiram Eldar, Sep 28 2018
STATUS
approved