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

1,1

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.

Links

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

Example

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

Mathematica

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

Prog

(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);

Crossrefs

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

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

Sequence in context: A280074 A359745 A086263 * A335071 A073143 A066613

Adjacent sequences: A355706 A355707 A355708 * A355710 A355711 A355712

Keyword

nonn

Author

Amiram Eldar, Jul 15 2022

Status

approved