A385652 -id:A385652 - cp's OEIS frontend

A385653 Least k such that A385652(k) = n.

2, 4, 8, 12, 18, 24, 27, 36, 48, 54, 72, 80, 90, 100, 120, 125, 135, 150, 160, 180, 196, 210, 224, 245, 252, 280, 294, 315, 336, 343, 350, 378, 392, 420, 441, 448, 490, 504, 525, 560, 567, 588, 630, 672, 686, 700, 735, 756, 784, 840, 875, 882, 896, 945, 980

Offset: 1

Pontus von Brömssen, Jul 06 2025

nonn

A385654(n) is uniquely popular on the interval [2,a(n)]; see A289662.

Equivalently, a(n) is the least k >= 2 such that A078899(k) = n.

Pontus von Brömssen, Table of n, a(n) for n = 1..10000

Cf. A006530, A078899, A289662, A385503, A385652, A385654.

gpf(n) = if (n==1,1, vecmax(factor(n)[,1])); \\ A006530
f(n) = my(v=vector(n, k, gpf(k)), s=Set(v)); vecmax(apply(x->#x, vector(#s, i, select(x->(x==s[i]), v)))); \\ A385652
a(n) = my(k=2); while (f(k) !=n, k++); k; \\ Michel Marcus, Jul 06 2025

A385654 Greatest prime factor of A385653(n).

Original entry on oeis.org

2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 13, 13, 13, 13, 13, 7, 13, 13, 13, 13, 13, 13

Offset: 1

Pontus von Brömssen, Jul 06 2025

nonn

A number appears in this sequence if and only if it is a uniquely popular prime; see A289662. a(n) is uniquely popular on the interval [2,A385653(n)].

Pontus von Brömssen, Table of n, a(n) for n = 1..10000

Cf. A006530, A289662, A385503, A385652, A385653.

gpf(n) = if (n==1,1, vecmax(factor(n)[,1])); \\ A006530
f(n) = my(v=vector(n, k, gpf(k)), s=Set(v)); vecmax(apply(x->#x, vector(#s, i, select(x->(x==s[i]), v)))); \\ A385652
a(n) = my(k=2); while (f(k) !=n, k++); gpf(k); \\ Michel Marcus, Jul 06 2025

A386007 Least k such that there are exactly n primes that are popular on the interval [2,k] (see A385503); i.e., exactly n primes share the lead as the most common greatest prime factor of the numbers 2..k.

Original entry on oeis.org

2, 3, 70, 2626355

Offset: 1

Pontus von Brömssen, Jul 14 2025

			a(3) = 70, because the 3 primes 3, 5, and 7 all occur A385652(70) = 10 times (the maximum) as the greatest prime factor of the numbers 2..70, and for earlier intervals there is never a tie between 3 numbers.
a(4) = 2626355, because the 4 primes 73, 83, 109, and 113 all occur A385652(2626355) = 7634 times (the maximum) as the greatest prime factor of the numbers 2..2626355, and for earlier intervals there is never a tie between 4 numbers.

Cf. A006530, A385503, A385652.

gpf[n_]:=FactorInteger[n][[-1,1]];a[n_]:=Module[{k=1},Until[Length[Commonest[gpf/@Range[2,k]]]==n,k++];k] (* James C. McMahon, Jul 20 2025 *)

cp's OEIS Frontend

A385653 Least k such that A385652(k) = n.

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A385654 Greatest prime factor of A385653(n).

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PARI

A386007 Least k such that there are exactly n primes that are popular on the interval [2,k] (see A385503); i.e., exactly n primes share the lead as the most common greatest prime factor of the numbers 2..k.

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