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

1,1

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