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A355712
Starts of runs of 4 consecutive numbers with the same number of 5-smooth divisors.
3
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
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
KEYWORD
nonn
AUTHOR
Amiram Eldar, Jul 15 2022
STATUS
approved