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

1,1

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.

Links

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

Example

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

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

Prog

(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);

Crossrefs

Cf. A355583.

Subsequence of A355710 and A355711.

Similar sequences: A006601, A332314, A332388.

Sequence in context: A134123 A234087 A049052 * A266039 A202614 A270855

Adjacent sequences: A355709 A355710 A355711 * A355713 A355714 A355715

Keyword

nonn

Author

Amiram Eldar, Jul 15 2022

Status

approved