A355712 Starts of runs of 4 consecutive numbers with the same number of 5-smooth divisors.

28374, 133623, 136374, 187623, 190374, 298374, 349623, 352374, 457623, 460374, 511623, 619623, 622374, 673623, 676374, 781623, 838374, 943623, 946374, 997623, 1000374, 1108374, 1159623, 1162374, 1267623, 1270374, 1321623, 1429623, 1432374, 1483623, 1486374, 1591623

Offset: 1

Author

Amiram Eldar, Jul 15 2022

Keywords

• nonn

Comments

Numbers k such that A355583(k) = A355583(k+1) = A355583(k+2) = A355583(k+3).

Are there runs of 5 consecutive numbers with the same number of 5-smooth divisors? There are no such runs below 10^10.

Examples

			28374 is a term since A355583(28374) = A355583(28375) = A355583(28376) = A355583(28377) = 4.
		

Links

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

Crossrefs

Cf. A355583.

Subsequence of A355710 and A355711.

Similar sequences: A006601, A332314, A332388.

Programs

Mathematica

f[n_] := Times @@ (1 + IntegerExponent[n, {2, 3, 5}]); s = {}; m = 4; fs = f /@ Range[m]; Do[If[Equal @@ fs, AppendTo[s, n - m]]; fs = Rest @ AppendTo[fs, f[n]], {n, m + 1, 10^6}]; s

PARI

s(n) = (valuation(n, 2) + 1) * (valuation(n, 3) + 1) * (valuation(n, 5) + 1);
s1 = s(1); s2 = s(2); s3 = s(3); for(k = 4, 1.6e6, s4 = s(k); if(s1 == s2 && s2 == s3 && s3 == s4, print1(k-3,", ")); s1 = s2; s2 = s3; s3 = s4);