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A101942 Sequence f[n,4], where f[n,b] is as defined below. 1
1, 2, 4, 8, 3, 6, 12, 24, 9, 18, 36, 72, 27, 54, 108, 216, 5, 10, 20, 40, 15, 30, 60, 120, 45, 90, 180, 360, 135, 270, 540, 1080, 25, 50, 100, 200, 75, 150, 300, 600, 225, 450, 900, 1800, 675, 1350 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..45.

FORMULA

Let n = Sum[b^(i-1) * c_{i}] where 1 <= i <=r of N, c_{r}!=0, n of N, c_{i} of {0, 1, ..., b-2, b-1}. Then f[n, b] := Product[prime(i)^c_{i}]] 1 <= i <= r. Formula: For all b>=2, k of N_{0} : f[b^k, b] = prime(k-1).

EXAMPLE

f[29,4] = 270 because 29 = 131_4 -> f[29,4] = 5^1 * 3^3 * 2^1;

f[5,2] = 10 because 5 = 101_2 -> f[5,2] = 5^1 * 3^0 * 2^1;

f[5,3] = 12 because 5 = 12_3 -> f[5,3] = 3^1 * 2^2;

f[0,b] = 1 because 0 = 0_b -> f[0,b] = 2^0.

MATHEMATICA

f[n_Integer, base_Integer] /; base >= 2 := Product[ Prime[i]^IntegerDigits[n, base][[Length[IntegerDigits[n, base]] + 1 - i]], {i, Length[IntegerDigits[n, base]]}] Table[f[i, 4], {i, 0, 45}]

PROG

(PARI)

f(n, b) = { my(d = digits(n, b), L = #d); prod(i=1, L, prime(i)^d[L+1-i]) }

apply(n -> f(n, 4), [0..45]) \\ Satish Bysany, Mar 07 2017

CROSSREFS

A060882 = f[2^n - 1, 2] - f[2^n, 2].

Sequence in context: A036118 A247555 A340730 * A344534 A050170 A087089

Adjacent sequences:  A101939 A101940 A101941 * A101943 A101944 A101945

KEYWORD

base,nonn

AUTHOR

Orges Leka (oleka(AT)students.uni-mainz.de), Dec 21 2004

STATUS

approved

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Last modified September 23 07:00 EDT 2021. Contains 347609 sequences. (Running on oeis4.)