A076532 Numbers n such that sopf(sigma(n)) = sigma(sopf(n)), where sopf(x) = sum of the distinct prime factors of x.

2, 90, 425, 490, 605, 630, 726, 735, 750, 816, 2250, 2695, 3185, 3234, 3420, 3822, 4176, 5096, 5250, 6591, 7644, 8470, 9100, 9425, 10296, 10780, 11616, 11638, 12321, 15750, 16940, 18096, 22736, 23276, 25578, 27360, 27783, 28500, 31900, 36400

Offset: 1

Author

Joseph L. Pe, Oct 18 2002

Keywords

• nonn

Examples

			sopf(sigma(90)) = sopf(234) = 18; sigma(sopf(90)) = sigma(10) = 18, hence 90 is a term of the sequence.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A008472, A075565, A075784, A075846, A076525, A076527, A076531, A076533.

Programs

Mathematica

p[n_] := Apply[Plus, Transpose[FactorInteger[n]][[1]]]; Select[Range[2, 10^4], p[DivisorSigma[1, # ]] == DivisorSigma[1, p[ # ]] &]

PARI

isok(n) = (n>1) && sigma(sopf(n)) == sopf(sigma(n)); \\ Michel Marcus, Oct 04 2019

Extensions

Edited and extended by Ray Chandler, Feb 13 2005