A107913 Numbers k that require three iterations of the sigma function to be >= 2*k.
9, 13, 25, 37, 43, 49, 61, 67, 73, 97, 109, 121, 151, 157, 163, 169, 181, 193, 211, 225, 229, 241, 277, 283, 289, 313, 331, 337, 361, 373, 397, 409, 421, 433, 457, 487, 523, 529, 541, 547, 577, 601, 613, 625, 631, 661, 673, 691, 709, 729, 733, 751, 757, 787
Offset: 1
Keywords
Examples
sigma(sigma(9)) = 14 but sigma(sigma(sigma(9))) = 24, so 9 is in the sequence.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale)
Programs
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Mathematica
is3Q[n_]:=Boole[#>=2n&/@NestList[DivisorSigma[1,#]&,n,3]]=={0,0,0,1}; Select[Range[ 800],is3Q] (* Harvey P. Dale, Jul 09 2023 *) -
PARI
is(n) = {my(m = n, nn = 2*n, c = 0); while(m < nn, m = sigma(m); c++); c == 3;} \\ Amiram Eldar, Mar 18 2024
Extensions
Offset 1 by Michel Marcus, Apr 25 2020