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A130075 Quotients (5^p - 3^p - 2^p)/p, where p = Prime(n). 4
6, 30, 570, 10830, 4422630, 93776970, 44871187170, 1003806502230, 518297165370030, 6422911941109705770, 150213298561349961630, 1966475018690546370358170, 1109139879321302763891656370 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

p divides 5^p - 3^p - 2^p = A130072(p) for prime p. p^(k+1) divides A130072(p^k) for prime p = {2,3,5,19} = A130076(n) and all k>0. 2 divides a(n). 3 divides a(n). 5 divides a(n) for n>1. 19 divides a(n) for n>2. 19^2 divides a(n) for n = {4,6,8,11,12,14,...} = A091178(n) n-th prime is of the form 6n+1; or Prime(n) = {7,13,19,31,37,43,...} = A002476 Primes of form 6n + 1.

LINKS

Table of n, a(n) for n=1..13.

FORMULA

a(n) = (5^Prime[n] - 3^Prime[n] - 2^Prime[n])/Prime[n]. a(n) = A130072(Prime(n))/Prime(n).

MATHEMATICA

Table[(5^Prime[n]-3^Prime[n]-2^Prime[n])/Prime[n], {n, 1, 20}]

(5^#-3^#-2^#)/#&/@Prime[Range[20]] (* Harvey P. Dale, May 02 2012 *)

CROSSREFS

Cf. A130072, A130073, A130074, A130076, A091178, A002476.

Sequence in context: A119634 A256545 A075591 * A066388 A222718 A200894

Adjacent sequences:  A130072 A130073 A130074 * A130076 A130077 A130078

KEYWORD

nonn

AUTHOR

Alexander Adamchuk, May 06 2007

STATUS

approved

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Last modified May 29 20:42 EDT 2020. Contains 334710 sequences. (Running on oeis4.)