A115560 -id:A115560 - cp's OEIS frontend

A115558 a(n) is the square root of A115557(n).

1, 7, 11, 13, 19, 23, 29, 31, 43, 47, 53, 73, 83, 97, 103, 113, 127, 157, 179, 197, 199, 223, 227, 233, 239, 241, 251, 257, 271, 281, 311, 316, 317, 333, 353, 389, 401, 409, 419, 421, 443, 449, 461, 467, 479, 491, 503, 509, 549, 563, 587, 593, 599, 617, 641

Offset: 1

Labos Elemer, Jan 25 2006

nonn

Giovanni Resta, Table of n, a(n) for n = 1..10000

Cf. A000005, A000203, A076360, A076361, A062068, A062069, A115557, A115559, A115560.

Select[Range[1000], DivisorSigma[0, DivisorSigma[1, #^2]] == DivisorSigma[1, DivisorSigma[0, #^2]] &] (* Amiram Eldar, Jan 28 2025 *)

isok(k) = numdiv(sigma(k^2)) == sigma(numdiv(k^2)); \\ Amiram Eldar, Jan 28 2025

The commutator [sigma, tau] is zero and a(n) is the square root of solutions. Both prime and composite numbers.

A115559 Nonprime terms of A115558.

Original entry on oeis.org

1, 316, 333, 549, 844, 963, 981, 1052, 1233, 1251, 1304, 1341, 1359, 1474, 1629, 1688, 1737, 1738, 1996, 2061, 2144, 2216, 2421, 2528, 2547, 2763, 2979, 3033, 3082, 3123, 3141, 3148, 3231, 3244, 3283, 3303, 3411, 3573, 3634, 3871, 3879, 3897, 3988, 4113

Offset: 1

Labos Elemer, Jan 25 2006

nonn

Giovanni Resta, Table of n, a(n) for n = 1..10000

Intersection of A018252 and A115558.

Cf. A000005, A000203, A076360, A076361, A062068, A062069, A115557, A115560.

Select[Range[5000], !PrimeQ[#] && DivisorSigma[0, DivisorSigma[1, #^2]] == DivisorSigma[1, DivisorSigma[0, #^2]] &] (* Amiram Eldar, Jan 28 2025 *)

isok(n)= !isprime(n) && (sigma(numdiv(n^2)) == numdiv(sigma(n^2))); \\ Michel Marcus, Dec 20 2013

The commutator [sigma, tau] is zero and a(n) is the square root of solutions. Moreover this square root is a nonprime number.

cp's OEIS Frontend

A115558 a(n) is the square root of A115557(n).

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