A378794 Numbers k such that tau(k) == 1 (mod(2*(tau(k^2 + k - 1)))), where tau(k) = A000005(k).

1, 16, 36, 100, 196, 225, 256, 441, 484, 625, 676, 1089, 1156, 1225, 1296, 2116, 2601, 3136, 3249, 3364, 3844, 4225, 5929, 6561, 7056, 7225, 7569, 8100, 8281, 8836, 9216, 10000, 11236, 12321, 13924, 14161, 14884, 15129, 16641, 17689, 17956, 19881, 20164, 20449

Offset

1,2

Comments

736 terms < 10^7 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).

Links

Table of n, a(n) for n=1..44.

Example

1 is a term because tau(1) = 1, tau(1 + 1 - 1) = 1 and 1 modulo 2 is 1.
16 is a term because tau(16) = 5, tau(256 + 16 - 1) = 2 and 5 modulo 4 is 1.
50 is not a term because tau(50) = 6, tau(2500 + 50 -1) = 2 and 6 modulo 4 is 2.

Prog

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

Crossrefs

Cf. A000005, A000040.

Cf. A378789, A378792.

Sequence in context: A022040 A074985 A229134 * A069262 A076956 A075369

Adjacent sequences: A378791 A378792 A378793 * A378795 A378796 A378797

Keyword

nonn,easy

Author

Claude H. R. Dequatre, Dec 07 2024

Status

approved