A355709 Numbers k such that k and k+1 have the same number of 3-smooth divisors.

2, 14, 21, 33, 38, 44, 50, 57, 69, 74, 80, 86, 93, 99, 105, 110, 116, 122, 129, 135, 141, 146, 158, 165, 171, 177, 182, 194, 201, 213, 218, 230, 237, 249, 254, 260, 266, 273, 285, 290, 296, 302, 309, 315, 321, 326, 332, 338, 345, 357, 362, 374, 381, 387, 393, 398

Offset: 1

Author

Amiram Eldar, Jul 15 2022

Keywords

• nonn

Comments

Numbers k such that A072078(k) = A072078(k+1).

This sequence is infinite since it includes all the numbers of the form 3*(2^(2*k+1)-1), with k>=1.

Examples

			2 is a term since A072078(2) = A072078(3) = 2.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A072078, A355710 (5-smooth analog).

Similar sequences: A005237, A006049, A332386, A343819, A344312, A344313, A344314, A348345.

Programs

Mathematica

s[n_] := Times @@ (1 + IntegerExponent[n, {2, 3}]); Select[Range[400], s[#] == s[#+1] &]

PARI

s(n) = (valuation(n, 2) + 1) * (valuation(n, 3) + 1);
s1 = s(1); for(k = 2, 400, s2 = s(k); if(s1 == s2, print1(k-1,", ")); s1 = s2);