A034884 Numbers k such that k < d(k)^2, where d(k) = A000005(k).

2, 3, 4, 6, 8, 10, 12, 14, 15, 16, 18, 20, 24, 28, 30, 32, 36, 40, 42, 48, 54, 56, 60, 72, 80, 84, 90, 96, 108, 120, 126, 132, 140, 144, 168, 180, 192, 210, 216, 240, 252, 288, 300, 336, 360, 420, 480, 504, 540, 720, 840, 1260

Offset

1,1

Comments

See comment in A175495. - Vladimir Shevelev, May 07 2013

The deficient terms are 2, 3, 4, 8, 10, 14, 15, 16, 32; the first perfect or abundant number not listed is 66 = 2 * 3 * 11; the only term not 7-smooth is 132 = 2^2 * 3 * 11; the largest not divisible by 6 is 140 = 2^2 * 5 * 7. - Peter Munn, Sep 19 2021

The union of this sequence and A276734 has 74 total terms which are all k with floor(sqrt(k)) <= d(k). - Bill McEachen, Apr 07 2023

Links

Table of n, a(n) for n=1..52.

Mathematica

Select[Range[1300], #<DivisorSigma[0, #]^2&] (* Harvey P. Dale, Apr 11 2014 *)

Prog

(PARI) isok(n) = (n < numdiv(n)^2) \\ Michel Marcus, Jun 07 2013

Crossrefs

Cf. A000005, A035033, A035034, A035035, A033950, A036763, A175495, A276734.

Sequence in context: A336367 A064377 A175495 * A137291 A032954 A158023

Adjacent sequences: A034881 A034882 A034883 * A034885 A034886 A034887

Keyword

nonn,fini,full

Author

Erich Friedman

Extensions

Labos Elemer added the last three terms and observes that this sequence is now complete.

Status

approved