A075867 Numbers k such that tau(k) = sigma(sopf(k)).

4, 12, 18, 27, 40, 180, 250, 300, 450, 704, 780, 924, 1120, 1170, 1320, 1344, 1386, 1400, 1950, 1960, 2025, 2970, 3125, 3192, 3234, 3500, 4080, 4455, 4725, 4760, 4896, 5070, 5082, 5625, 5720, 6615, 6860, 7182, 7280, 7875, 8250, 8280, 8505, 8704

Offset

1,1

Links

David A. Corneth, Table of n, a(n) for n = 1..10000 (first 6300 terms from Robert Israel)

Example

tau(40) = number of divisors of 40 = 8; sigma(sum of prime factors of 40) = sigma(2 + 5) = 8. Hence 40 is a term of the sequence.

Maple

filter:= proc(n) uses numtheory;
  tau(n) = sigma(convert(factorset(n), `+`))
end proc:
select(filter, [$1..10^4]); # Robert Israel, Jun 09 2020

Mathematica

Select[Range[2, 10^4], DivisorSigma[1, Apply[Plus, Transpose[FactorInteger[ # ]][[1]]]] == DivisorSigma[0, # ] &]

Prog

(PARI) is(n) = my(f = factor(n)); numdiv(f) == sigma(vecsum(f[, 1])) \\ David A. Corneth, Jun 09 2020

Crossrefs

Cf. A000005 (tau), A000203 (sigma), A000586, A008472 (sopf).

Sequence in context: A063679 A340597 A325234 * A071929 A008037 A301251

Adjacent sequences: A075864 A075865 A075866 * A075868 A075869 A075870

Keyword

nonn

Author

Joseph L. Pe, Oct 15 2002

Extensions

Offset changed by Robert Israel, Jun 09 2020

Status

approved