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A020493
Numbers k such that d(k) (number of divisors) divides phi(k) (Euler function) divides sigma(k) (sum of divisors).
2
1, 3, 15, 30, 35, 56, 70, 78, 105, 140, 168, 190, 210, 248, 264, 357, 420, 570, 616, 630, 714, 744, 812, 840, 910, 1045, 1240, 1485, 1672, 1848, 2090, 2214, 2436, 2580, 2730, 3080, 3135, 3339, 3596, 3720, 3956, 4064, 4180, 4522, 4674, 5016, 5049, 5278, 5396
OFFSET
1,2
COMMENTS
Numbers k such that sigma_0(k) divides phi(k) divides sigma_1(k).
REFERENCES
David Wells, Curious and interesting numbers, Penguin Books, p. 130.
LINKS
EXAMPLE
210 has 16 divisors, which divides phi(210) = 48, which in turn divides sigma(210) = 576, so 210 is a term of the sequence.
MATHEMATICA
q[n_] := And @@ IntegerQ /@ Ratios @ {DivisorSigma[0, n], EulerPhi[n], DivisorSigma[1, n]}; Select[Range[6000], q] (* Amiram Eldar, Apr 13 2024 *)
PROG
(PARI) for(n=1, 1e3, if(sigma(n)%eulerphi(n)==0, if(sigma(n)%numdiv(n)==0, if(eulerphi(n)%numdiv(n)==0, print1(n, ", "))))) \\ Felix Fröhlich, Aug 08 2014
CROSSREFS
Intersection of A020491 and A020492.
Sequence in context: A202506 A053519 A039666 * A087183 A297851 A298088
KEYWORD
nonn
EXTENSIONS
Wells incorrectly has 52 instead of 56.
STATUS
approved