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A295078 Numbers n > 1 such that n and sigma(n) have the same smallest and simultaneously largest prime factors. 2
6, 28, 40, 84, 120, 140, 224, 234, 270, 420, 468, 496, 672, 756, 936, 1080, 1120, 1170, 1372, 1488, 1550, 1638, 1782, 1862, 2176, 2340, 2480, 2574, 3100, 3250, 3276, 3360, 3472, 3564, 3724, 3744, 3780, 4116, 4464, 4598, 4650, 4680, 5148, 5456, 5586, 6048, 6200 (list; graph; refs; listen; history; text; internal format)
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

Intersection of A071834 and A295076.

Numbers n such that A020639(n) = A020639(sigma(n)) and simultaneously A006530(n) = A006530(sigma(n)).

Numbers n such that A020639(n) = A071189(n) and simultaneously A006530(n) = A071190(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

Cf. A000203, A006530, A007691, A020639, A027598, A071189, A071190, A295076.

Sequence in context: A242344 A247111 A071834 * A055196 A323752 A120624

Adjacent sequences:  A295075 A295076 A295077 * A295079 A295080 A295081

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

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Last modified February 16 14:47 EST 2019. Contains 320163 sequences. (Running on oeis4.)