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A237613 Numbers k such that tau(sigma(tau(k))) = sigma(tau(sigma(k))), where tau is A000005 and sigma is A000203. 1
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 (list; graph; refs; listen; history; text; internal format)
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 A117678 A167045

Adjacent sequences:  A237610 A237611 A237612 * A237614 A237615 A237616

KEYWORD

nonn

AUTHOR

Paolo P. Lava, Feb 10 2014

STATUS

approved

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Last modified October 16 13:51 EDT 2019. Contains 328093 sequences. (Running on oeis4.)