A378792 Numbers k such that tau(k) == 1 (mod(2*(tau(prime(k) - k + 1)))), where tau(k) = A000005(k).

1, 196, 225, 441, 484, 625, 1089, 1156, 1225, 1296, 1444, 3025, 3249, 3844, 4225, 5929, 6561, 7225, 7396, 7569, 8281, 11236, 12321, 13225, 13924, 15129, 16641, 17689, 20164, 21025, 24025, 25281, 25600, 34225, 34969, 40401, 42025, 47089, 50625, 51076, 55225

Offset: 1

Author

Claude H. R. Dequatre, Dec 07 2024

Keywords

• nonn
• easy

Comments

118 terms < 5*10^5 were found.

All terms are squares because their number of divisors is odd (see formula field in A000005: a(n) is odd iff n is square).

Examples

			1 is a term because tau(1) = 1, tau(2 -1  + 1) = 2 and 1 modulo 4 is 1.
196 is a term because tau(196) = 9, tau(1193 - 196 + 1) = 4 and 9 modulo 8 is 1.
200 is not a term because tau(200) = 12, tau(1223 -200 + 1) = 11 and 12 modulo 22 = 12.
		

Crossrefs

Cf. A000005, A000040, A011757.

Cf. A378789, A378794.

Programs

PARI

isok(k)=my(d_1=numdiv(k),d_2=numdiv(prime(k)-k+1));d_1%(2*d_2)==1;
for(k=1,1000,if(isok(k),print1(k", ")))