A307245 First occurrence of n in A306722.

11, 1, 3, 10, 27, 60, 72, 120, 180, 270, 480, 252, 1155, 720, 792, 1260, 630, 1050, 4590, 1680, 1320, 7980, 3780, 4680, 5880, 5040, 5460, 4620, 9180, 10080, 10710, 6930, 9240, 7560, 21420, 20790, 27300, 52080, 15120, 13860, 48510, 23940, 62370, 46200, 16380, 30030

Offset: 0

Author

Bernard Schott and Robert G. Wilson v, Mar 30 2019

Keywords

• nonn

Comments

Record values: 11, 27, 60, 72, 120, 180, 270, 480, 1155, 1260, 4590, 7980, 9180, 10080, 10710, 21420, 27300, 52080, 62370, 191520, 207480, 214200, 428400, ..., .

Examples

			a(0) = 11  because (2*11)^2 = 484 is the smaller integer that can't be written as (p-1)*(q-1) with p,q primes, p < q.
a(3) = 10 because (2*10)^2 = 400 is the smaller integer such that the Diophantine equation (p-1)*(q-1) = 400 has three solutions: (p,q) = (2,401) = (5,101) = (11,41); also, phi(2*401) = phi(5*101) = phi(11*41) = 20^2.
		

Links

• Robert G. Wilson v, Table of n, a(n) for n = 0..876

Crossrefs

Cf. A039770, A247129, A306722.

Programs

Mathematica

f[n_] := Length@ Select[ Divisors[ 4n^2], # < 2n && PrimeQ[# +1] && PrimeQ[4n^2/# +1] &]; t[_] := 0; k = 1; While[k < 100000, a = f@k; If[t[a] == 0, t[a] = k]; k++]; t@# & /@ Range[0, 50]