A237613 Numbers k such that tau(sigma(tau(k))) = sigma(tau(sigma(k))), where tau is A000005 and sigma is A000203.

1, 4, 9, 25, 81, 289, 1681, 3481, 5041, 7921, 10201, 17161, 27889, 29929, 85849, 146689, 331776, 458329, 491401, 552049, 579121, 597529, 683929, 703921, 734449, 786432, 829921, 1190281, 1203409, 1352569, 1394761, 1423249, 1481089, 1885129, 2036329, 2211169

Offset

1,2

Comments

The squares of the terms of A053182 are a subset of this sequence. In fact, in general, if p is prime we have tau(p)=2 and tau(p^2)=3. Therefore tau(p^2)=3 -> sigma(3)=4 -> tau(4)=tau(2^2)=3 and if p belongs to A053182 we also have that sigma(p^2)=p^2+p+1 (prime) -> tau(p^2+p+1)=2 -> sigma(2)=3.

Links

Amiram Eldar, Table of n, a(n) for n = 1..100

Maple

with(numtheory); P:=proc(q) local n;
for n from 1 to q do
  if tau(sigma(tau(n)))=sigma(tau(sigma(n))) then print(n); fi;
od; end: P(10^6);

Mathematica

s = {}; Do[If[DivisorSigma[1, DivisorSigma[0, DivisorSigma[1, n]]] == DivisorSigma[0, DivisorSigma[1, DivisorSigma[0, n]]], AppendTo[s, n]], {n, 1, 2500000}]; s (* Amiram Eldar, Aug 17 2019 *)

Prog

(PARI) s=[]; for(n=1, 2500000, if(sigma(sigma(sigma(n, 0)), 0) == sigma(sigma(sigma(n), 0)), s=concat(s, n))); s \\ Colin Barker, Feb 10 2014
(Magma) [k:k in [1..2300000]| #Divisors(SumOfDivisors(#Divisors(k))) eq SumOfDivisors(#Divisors(SumOfDivisors(k)))]; // Marius A. Burtea, Aug 17 2019

Crossrefs

Cf. A000005, A000203, A053182.

Sequence in context: A317975 A307396 A028400 * A220444 A355799 A117678

Adjacent sequences: A237610 A237611 A237612 * A237614 A237615 A237616

Keyword

nonn

Author

Paolo P. Lava, Feb 10 2014

Status

approved