A295076 Numbers n > 1 such that n and sigma(n) have the same smallest prime factor.

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

Offset: 1

Author

Jaroslav Krizek, Nov 13 2017

Keywords

• nonn

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).

Examples

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

Crossrefs

Cf. A000203, A020639, A071189, A088829, A295078.

Cf. A071834 (numbers n such that n and sigma(n) have the same largest prime factor).

Programs

Magma

[n: n in [2..1000000] | Minimum(PrimeDivisors(SumOfDivisors(n))) eq Minimum(PrimeDivisors(n))]

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 *)

PARI

isok(n) = factor(n)[1,1] == factor(sigma(n))[1,1]; \\ Michel Marcus, Nov 14 2017

Extensions

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