A188427 -id:A188427 - cp's OEIS frontend

A112763 Smallest prime factor of the n-th 5-smooth number.

1, 2, 3, 2, 5, 2, 2, 3, 2, 2, 3, 2, 2, 2, 2, 5, 3, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 3, 2, 3, 2, 2, 2, 2, 2, 5, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 2, 2, 3, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3

Offset: 1

Reinhard Zumkeller, Sep 18 2005

nonn

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

Cf. A020639, A051037, A086410, A112755, A112764, A188425, A188426, A188427.

[1] cat [Min(PrimeDivisors(k)): k in [2..1500]| PrimeDivisors(k) subset [2, 3, 5]]; // Marius A. Burtea, Feb 07 2020

FactorInteger[#][[1, 1]] & /@ Select[Range[3000], Last @ Map[First, FactorInteger[#]] <= 5 &] (* Amiram Eldar, Feb 07 2020 *)

a(n) = A020639(A051037(n));
a(n) <= A112764(n) <= 5.
a(A188427(n)) = 5 for n > 1. - David A. Corneth, Feb 07 2020

A188425 Position of 2^n in A051037 (5-smooth numbers).

Original entry on oeis.org

1, 2, 4, 7, 12, 19, 27, 38, 52, 68, 87, 110, 137, 167, 201, 240, 284, 332, 386, 446, 511, 582, 660, 745, 836, 934, 1041, 1155, 1277, 1407, 1545, 1692, 1849, 2015, 2190, 2376, 2571, 2777, 2994, 3222, 3461, 3711, 3974, 4249, 4535, 4834, 5147, 5473, 5811, 6164, 6531, 6911, 7306, 7716, 8142, 8582, 9039, 9511, 9999, 10503, 11024, 11563, 12119, 12692, 13283, 13892, 14519

Offset: 0

Zak Seidov, Mar 30 2011

nonn

			2^0 = 1 = A051037(1), hence a(0) = 1.
a(25) = 934 because 2^25 = 33554432 = A051037(934).

Zak Seidov, Table of n, a(n) for n = 0..200

Cf. A051037, A188426, A188427 (positions of powers of 3 and 5 in A051037).

A051037(a(n)) = 2^n.

a(n) ~ c * n^3, where c = log(2)^2/(6*log(3)*log(5)) = 0.045287775775708... - Vaclav Kotesovec and Amiram Eldar, Sep 22 2024

A188426 Position of 3^n in A051037 (5-smooth numbers).

Original entry on oeis.org

1, 3, 8, 17, 31, 50, 77, 112, 157, 211, 276, 355, 448, 554, 676, 815, 973, 1149, 1344, 1561, 1801, 2064, 2351, 2663, 3003, 3371, 3766, 4190, 4647, 5135, 5657, 6212, 6802, 7430, 8094, 8797, 9539, 10322, 11147, 12014, 12925, 13881, 14883, 15933, 17031, 18178, 19375, 20624, 21925, 23281, 24690

Offset: 0

Zak Seidov, Mar 31 2011

nonn

Zak Seidov, Table of n, a(n) for n = 0..150

Cf. A051037, A188425, A188427 (powers of 2 and 5).

A051037(a(n)) = 3^n.

a(n) ~ c * n^3, where c = log(3)^2/(6*log(2)*log(5)) = 0.180317536836709... - Vaclav Kotesovec and Amiram Eldar, Sep 22 2024

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A112763 Smallest prime factor of the n-th 5-smooth number.

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A188425 Position of 2^n in A051037 (5-smooth numbers).

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A188426 Position of 3^n in A051037 (5-smooth numbers).

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