login
A075867
Numbers k such that tau(k) = sigma(sopf(k)).
1
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
KEYWORD
nonn
AUTHOR
Joseph L. Pe, Oct 15 2002
EXTENSIONS
Offset changed by Robert Israel, Jun 09 2020
STATUS
approved