A379123 a(n) = A379113(A379121(n)), where A379121 gives those odd squares k for which A379113(k) > 1.

9, 121, 9, 9, 81, 1521, 9, 9, 49, 49, 81, 9, 9, 625, 49, 49, 9, 961, 9, 9, 9, 961, 961, 49, 9, 961, 961, 169, 961, 961, 16129, 49, 49, 961, 961, 961, 961, 961, 49, 9, 9, 9, 9, 625, 961, 16129, 16129, 961, 961, 961, 49, 9, 49, 16129, 961, 49, 961, 9, 49, 49, 49, 49, 9, 9, 9, 9, 49, 9, 16129, 9, 9, 49, 49, 9, 49, 9

Offset

1,1

Comments

All terms are odd squares (A016754) by definition.

Among the initial 2025 terms, only the following 12 terms occur:

Term Occurs Where

n times

---------------------------------------------------------------

9 699

49 665

81 2 a(5) and a(11)

121 1 a(2)

169 2 a(28) and a(926)

625 9 at n=14, 44, 85, 110, 155, 447, 654, 896, 1217.

961 390

1521 1 a(6) NB: 1521 = 9*169.

8649 1 a(1087). NB: 8649 = 9*961.

16129 246

67092481 8 First occurrence at a(1120)

3287531569 1 a(1636). NB: 3287531569 = 49*67092481.

Questions: Is this sequence infinite? Do all terms of A133049 eventually appear here? Or any 4th or higher powers of Mersenne and other primes, apart from 81 and 625?

Links

Antti Karttunen, Table of n, a(n) for n = 1..2025

Index entries for sequences defined by congruent products between domains N and GF(2)[X].

Index entries for sequences related to polynomials in ring GF(2)[X].

Index entries for sequences related to sigma(n).

Formula

a(n) = A379121(n) / A379124(n).

Example

See examples in A379121.

Prog

(PARI) forstep(n=1, 2^18, 2, d=A379113(n^2); if(d>1, print1(d, ", ")));

Crossrefs

Cf. A016754, A114390, A133049, A379113, A379121, A379124, A379125.

Sequence in context: A024487 A002691 A387809 * A234320 A157930 A259836

Adjacent sequences: A379120 A379121 A379122 * A379124 A379125 A379126

Keyword

nonn

Author

Antti Karttunen, Dec 18 2024

Status

approved