A332218 Numbers k such that A332221(k) = A156552(sigma(k)) is 2*{an odd square}.

2, 162, 441, 2704, 4225, 275194921

Offset

1,1

Comments

Any even term of A332216 must occur also in this sequence.

Links

Table of n, a(n) for n=1..6.

Index entries for sequences related to sigma(n)

Example

  a(n)              -> sigma(a(n))              -> A156552(sigma(a(n)))
     2 = 2^1 * 1^2  ->    3 = 3^1               ->      2 = 2^1 * 1^1,
   162 = 2^1 * 3^4  ->  363 = 3^1 * 11^2        ->     98 = 2^1 * 7^2,
   441 = 3^2 * 7^2  ->  741 = 3^1 * 13^1 * 19^1 ->    578 = 2^1 * 17^2,
  2704 = 2^4 * 13^2 -> 5673 = 3^1 * 31^1 * 61^1 -> 526338 = 2^1 * 3^6 * 19^2,
  4225 = 5^2 * 13^2 -> 5673 = 3^1 * 31^1 * 61^1 -> 526338 = 2^1 * 3^6 * 19^2,
and
275194921 = 53^2 * 313^2 -> 281384229 = 3^1 * 7^1 * 181^2 * 409^1 -> 9671406556943421676716050 = 2^1 * 5^2 * 7^2 * 62829235873^2.

Mathematica

Select[Range@ 5000, And[IntegerQ[#], OddQ[#]] &@ Sqrt[#/2] &@ Floor@ Total@ Flatten@ MapIndexed[#1 2^(#2 - 1) &, Flatten[Table[2^(PrimePi@ #1 - 1), {#2}] & @@@ FactorInteger@ DivisorSigma[1, #]]] &] (* Michael De Vlieger, Feb 12 2020 *)

Prog

(PARI)
\\ Needs also code from A156552:
istosq(n) = ((1==valuation(n, 2))&&issquare(n/2));
for(n=1, 2^25, if(istosq(A156552(sigma(n*n))), print1(n*n, ", ")); if(istosq(A156552(sigma(2*n*n))), print1(2*n*n, ", ")));

Crossrefs

Cf. A000203, A156552, A332216, A332217, A332221.

Subsequence of A332217 ⊂ A067051 ⊂ A028982.

Sequence in context: A272244 A178575 A069580 * A202107 A300363 A109420

Adjacent sequences: A332215 A332216 A332217 * A332219 A332220 A332221

Keyword

nonn,more

Author

Antti Karttunen, Feb 11 2020

Status

approved