A322676 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.

1, 3, 6, 12, 24, 48, 72, 120, 168, 240, 360, 720, 1440, 2160, 2520, 4320, 5040, 7560, 10080, 15120, 20160, 27720, 30240, 55440, 75600, 83160, 110880, 151200, 166320, 332640, 665280, 831600, 1330560, 1441440, 1663200, 2162160, 2882880, 3326400, 4324320, 6486480, 8648640

Offset: 1

Author

Daniel Suteu, Dec 23 2018

Keywords

• nonn

Comments

Position of records in A072627.

Crossrefs

Cf. A072627, A202727, A322678.

Programs

Mathematica

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

PARI

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