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

Author

Antti Karttunen, Dec 18 2024

Keywords

• nonn

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?

Examples

			See examples in A379121.
		

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).

Crossrefs

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

Programs

PARI

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

Formula

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