A355710 Numbers k such that k and k+1 have the same number of 5-smooth divisors.

2, 21, 33, 34, 38, 57, 85, 86, 93, 94, 104, 116, 122, 141, 145, 146, 154, 158, 171, 177, 182, 189, 201, 205, 213, 214, 218, 237, 265, 266, 273, 296, 302, 321, 326, 332, 334, 338, 344, 357, 362, 381, 385, 387, 393, 394, 398, 417, 445, 446, 453, 454, 475, 476, 482

Offset: 1

Author

Amiram Eldar, Jul 15 2022

Keywords

• nonn

Comments

Numbers k such that A355583(k) = A355583(k+1).

Examples

			2 is a term since A355583(2) = A355583(3) = 2.
		

Links

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

Crossrefs

Cf. A355583, A355709 (3-smooth analog).

Subsequences: A355711, A355712.

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

Programs

Mathematica

s[n_] := Times @@ (1 + IntegerExponent[n, {2, 3, 5}]); Select[Range[500], s[#] == s[#+1] &]

PARI

s(n) = (valuation(n, 2) + 1) * (valuation(n, 3) + 1) * (valuation(n, 5) + 1);
s1 = s(1); for(k = 2, 500, s2 = s(k); if(s1 == s2, print1(k-1,", ")); s1 = s2);