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Numbers k > 0 such that k has more divisors d, such that d-1 is prime, than any other smaller positive number, with a(1) = 1.
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%I #21 Dec 17 2024 16:35:40

%S 1,3,6,12,24,48,72,120,168,240,360,720,1440,2160,2520,4320,5040,7560,

%T 10080,15120,20160,27720,30240,55440,75600,83160,110880,151200,166320,

%U 332640,665280,831600,1330560,1441440,1663200,2162160,2882880,3326400,4324320,6486480,8648640

%N Numbers k > 0 such that k has more divisors d, such that d-1 is prime, than any other smaller positive number, with a(1) = 1.

%C Position of records in A072627.

%t DeleteDuplicates[Table[{n,Count[Divisors[n]-1,_?PrimeQ]},{n,87*10^5}],GreaterEqual[#1[[2]],#2[[2]]]&][[;;,1]] (* _Harvey P. Dale_, Dec 17 2024 *)

%o (PARI) r=-1; for(n=1, 10^6, t=sumdiv(n, d, isprime(d-1)); if(t>r, r=t; print1(n, ", ")));

%Y Cf. A072627, A202727, A322678.

%K nonn

%O 1,2

%A _Daniel Suteu_, Dec 23 2018