OFFSET
1,1
COMMENTS
All even perfect numbers are terms.
Conjecture: A007691 (multiply-perfect numbers) is a subsequence.
Note that an odd perfect number (if it exists) would be a counterexample to the conjecture. - Robert Israel, Jan 08 2018
Numbers n such that A020639(n) = A020639(sigma(n)) and simultaneously A006530(n) = A006530(sigma(n)).
Supersequence of A027598.
LINKS
Jaroslav Krizek, Table of n, a(n) for n = 1..1000
EXAMPLE
40 = 2^3*5 and sigma(40) = 90 = 2*3^2*5 hence 40 is in the sequence.
The first odd term is 29713401 = 3^2 * 23^2 * 79^2; sigma(29713401) = 45441669 = 3*7^3*13*43*79.
MAPLE
filter:= proc(n) local f, s; uses numtheory;
f:= factorset(n);
s:= factorset(sigma(n));
min(f) = min(s) and max(f)=max(s)
end proc:
select(filter, [$2..10^4]); # Robert Israel, Jan 08 2018
MATHEMATICA
Rest@ Select[Range@ 6200, SameQ @@ Map[{First@ #, Last@ #} &@ FactorInteger[#][[All, 1]] &, {#, DivisorSigma[1, #]}] &] (* Michael De Vlieger, Nov 13 2017 *)
PROG
(Magma) [n: n in [2..10000] | Minimum(PrimeDivisors(n)) eq Minimum(PrimeDivisors(SumOfDivisors(n))) and Maximum(PrimeDivisors(n)) eq Maximum(PrimeDivisors(SumOfDivisors(n)))]
(PARI) isok(n) = if (n > 1, my(fn = factor(n)[, 1], fs = factor(sigma(n))[, 1]); (vecmin(fn) == vecmin(fs)) && (vecmax(fn) == vecmax(fs))); \\ Michel Marcus, Jan 08 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Nov 13 2017
EXTENSIONS
Added condition n>1 to definition. Corrected b-file. - N. J. A. Sloane, Feb 03 2018
STATUS
approved