A232093 Position of 7^n among 7-smooth numbers (A002473).

1, 7, 30, 87, 202, 403, 726, 1214, 1911, 2874, 4158, 5832, 7968, 10640, 13933, 17937, 22747, 28464, 35195, 43054, 52162, 62644, 74630, 88257, 103671, 121020, 140462, 162155, 186267, 212973, 242453, 274894, 310483, 349420, 391909, 438161, 488388, 542814, 601667, 665181, 733594, 807154, 886109, 970720, 1061252, 1157972, 1261156, 1371084, 1488047, 1612341

Offset: 0

Author

Zak Seidov, Nov 18 2013

Keywords

• nonn

Comments

Note that all powers of 7 are terms in A002473.

Polynomial of fourth order is sufficient for very accurate approximation of a(n).

Examples

			A002473(a(1)) = A002473(7) = 7.
A002473(a(2)) = A002473(30) = 49 = 7^2.
A002473(a(200)) = A002473(411921660) = 7^200.
		

Links

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

Crossrefs

Cf. A000420, A002473.

Programs

Mathematica

ss7 = {}; Do[m = 7^n; s = Sum[1 + Floor[Log[2, 7^(n - k)/5^i/3^j]], {k, 0, n}, {i, 0, Log[5, 7^(n - k)]}, {j, 0, Log[3, 7^(n - k)/5^i]}]; AppendTo[ss7, {n, s}], {n, 0, 50}]; ss7

Formula

a(n) ~ c * n^4, where c = log(7)^3/(24*log(2)*log(3)*log(5)) = 0.250503020417439... - Vaclav Kotesovec and Amiram Eldar, Sep 22 2024