A275196 Odd numbers n such that sigma(n) does not divide sigma(n^3).

9, 25, 27, 49, 63, 75, 81, 99, 117, 121, 125, 135, 147, 153, 169, 171, 175, 207, 225, 243, 245, 261, 275, 289, 297, 325, 333, 343, 361, 363, 369, 375, 387, 405, 425, 441, 475, 477, 507, 513, 525, 529, 531, 539, 549, 567, 575, 603, 605, 625, 637, 639, 675, 693, 711, 725, 729

Offset

1,1

Comments

All terms are composite since sigma(p) = p + 1 and sigma(p^3) = p^3 + p^2 + p + 1 = (p + 1)(p^2 + 1) for p prime.

An odd number n with prime factorization Product_i p_i^(e_i) is in this sequence if and only if Product_i ((p_i^(3*e_i + 1) - 1)/(p_i^(e_i + 1) - 1)) is not an integer.

Nonsquare terms of this sequence are 27, 63, 75, 99, 117, 125, 135, 147, 153, 171, 175, 207, 243, 245, 261, 275, ...

Terms that are not perfect powers are 63, 75, 99, 117, 135, 147, 153, 171, 175, 207, 245, 261, 275, 297, 325, 333, 363, 369, 375, ...

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Example

63 is a term because sigma(63^3) = 437200 is not divisible by sigma(63) = 104.

Mathematica

Select[2Range[400] - 1, Not[Divisible[DivisorSigma[1, #^3], DivisorSigma[1, #]]] &] (* Alonso del Arte, Jul 20 2016 *)

Prog

(PARI) isok(n) = sigma(n^3) % sigma(n) != 0 && n % 2 == 1

Crossrefs

Cf. A000203, A175926.

Sequence in context: A053850 A225498 A020210 * A325373 A062739 A075109

Adjacent sequences: A275193 A275194 A275195 * A275197 A275198 A275199

Keyword

nonn

Author

Altug Alkan, Jul 20 2016

Status

approved