A076361 Numbers k such that d(sigma(k)) = sigma(d(k)).

1, 3, 44, 49, 66, 68, 70, 76, 99, 121, 124, 147, 153, 164, 169, 170, 171, 172, 243, 245, 268, 275, 279, 361, 363, 387, 425, 475, 507, 529, 564, 603, 620, 644, 652, 724, 775, 841, 844, 845, 873, 891, 927, 948, 961, 964, 1075, 1083, 1132, 1324, 1348, 1377

Offset: 1

Author

Labos Elemer, Oct 08 2002

Keywords

• easy
• nonn

Comments

Solutions to A076360(x) = 0.

Assuming Schinzel's hypothesis is true, the sequence is infinite. That conjecture implies that there are infinitely many primes p for which (p^2 + p + 1)/3 is prime. (E.g., p = 7, 13, 19, 31, 43, 73, 97, ...) For such p, we have d(sigma(p^2)) = d(p^2+p+1) = 4 and sigma(d(p^2)) = sigma(3) = 4, so p^2 is in the sequence. - Dean Hickerson, Jan 24 2006

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10029
• Eric Weisstein's World of Mathematics, Schinzel's hypothesis.

Crossrefs

Cf. A000005, A000203.

Programs

Mathematica

d0[x_] := DivisorSigma[0, x] d1[x_] := DivisorSigma[1, x] Do[s=d0[d1[n]]-d1[d0[n]]; If[s==0, Print[n]], {n, 1, 10000}]
Select[Range[1380],DivisorSigma[0, DivisorSigma[1, #]] == DivisorSigma[1, DivisorSigma[0, #]] &] (* Jayanta Basu, Mar 26 2013 *)

PARI

is(n)=numdiv(sigma(n))==sigma(numdiv(n)) \\ Charles R Greathouse IV, Jun 25 2013