A281664 Numbers k such that A000005(k) = A000005(A000217(k)).

1, 2, 6, 10, 18, 22, 30, 42, 46, 58, 66, 70, 78, 82, 102, 106, 126, 130, 138, 150, 162, 166, 178, 190, 198, 210, 222, 226, 238, 250, 262, 270, 282, 306, 310, 330, 346, 358, 366, 378, 382, 418, 430, 438, 442, 462, 466, 478, 486, 490, 498, 502, 522, 546, 562

Offset: 1

Author

Colin Barker, Jan 26 2017

Keywords

• nonn

Comments

Numbers k such that the number of divisors of k is equal to the number of divisors of k*(k+1)/2.

Links

• Colin Barker, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000005, A000217, A006093, A045326.

Programs

Maple

a:= proc(n) option remember; local p; p:= a(n-1)+2;
      while irem(p, 4)<>3 do p:= nextprime(p) od; p-1
    end: a(1):=1:
seq(a(n), n=1..100);  # Alois P. Heinz, Jan 27 2017

Mathematica

Select[Range@ 562, DivisorSigma[0, #] == DivisorSigma[0, PolygonalNumber@ #] &] (* Michael De Vlieger, Jan 27 2017, Version 10.4 *)

PARI

select(n->numdiv(n)==numdiv(n*(n+1)/2), vector(1000, n, n))

Formula

a(n) = A045326(n) - 1. - Alois P. Heinz, Jan 27 2017