

A295076


Numbers n > 1 such that n and sigma(n) have the same smallest prime factor.


1



6, 10, 12, 14, 20, 22, 24, 26, 28, 30, 34, 38, 40, 42, 44, 46, 48, 52, 54, 56, 58, 60, 62, 66, 68, 70, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120, 122, 124, 126, 130, 132, 134, 136, 138, 140, 142, 146, 148
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OFFSET

1,1


COMMENTS

Supersequence of A088829; this sequence contains also odd numbers: 441, 1521, 3249, 3969, 8649, 11025, ...
Even terms of A000396 (perfect numbers) are a subsequence.
Subsequence of A295078.
Numbers n such that A020639(n) = A020639(sigma(n)).
Numbers n such that A020639(n) = A071189(n).


LINKS

Table of n, a(n) for n=1..60.


EXAMPLE

30 = 2*3*5 and sigma(30) = 72 = 2^3*3^2 hence 30 is in the sequence.


MAPLE

select(t > min(numtheory:factorset(t))=min(numtheory:factorset(numtheory:sigma(t))), [$2..1000]); # Robert Israel, Nov 14 2017


MATHEMATICA

Rest@ Select[Range@ 150, SameQ @@ Map[FactorInteger[#][[1, 1]] &, {#, DivisorSigma[1, #]}] &] (* Michael De Vlieger, Nov 13 2017 *)


PROG

(MAGMA) [n: n in [2..1000000]  Minimum(PrimeDivisors(SumOfDivisors(n))) eq Minimum(PrimeDivisors(n))]
(PARI) isok(n) = factor(n)[1, 1] == factor(sigma(n))[1, 1]; \\ Michel Marcus, Nov 14 2017


CROSSREFS

Cf. A000203, A020639, A071189, A088829, A295078.
Cf. A071834 (numbers n such that n and sigma(n) have the same largest prime factor).
Sequence in context: A175397 A129493 A036350 * A088829 A036348 A100368
Adjacent sequences: A295073 A295074 A295075 * A295077 A295078 A295079


KEYWORD

nonn


AUTHOR

Jaroslav Krizek, Nov 13 2017


EXTENSIONS

Added n>1 to definition  N. J. A. Sloane, Feb 03 2018


STATUS

approved



