cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A276092 a(n) = Product_{i=1..n} prime(i)^(prime(i)-1), a(0)=1.

This page as a plain text file.
%I A276092 #19 Aug 31 2016 09:58:01
%S A276092 1,2,18,11250,1323551250,34329510752434301250,
%T A276092 799811863723341113907011901401250,
%U A276092 38919798565076223182552300534870824616780123359001250,4052615498709835178737678586220586796222761283625319842830388618784835051250,3679152532021669595137666762315244807517735994898621013565758767014111825486079213219685771368099483111250
%N A276092 a(n) = Product_{i=1..n} prime(i)^(prime(i)-1), a(0)=1.
%C A276092 Cumulative product of A036878 (after a(0)). - _Rick L. Shepherd_, Aug 23 2016
%F A276092 a(n) = Product_{i=1..n} prime(i)^(prime(i)-1).
%F A276092 a(0) = 1; and for n >= 1, a(n) = a(n-1) * A000040(n)^(A000040(n)-1).
%F A276092 a(n) = A276086(A057588(n)).
%e A276092 For n=0 we have an empty product, thus a(0) = 1.
%e A276092 For n=1, a(1) = 2^1.
%e A276092 For n=2, a(2) = 2^1 * 3^2 = 18.
%e A276092 For n=3, a(3) = 2^1 * 3^2 * 5^4 = 11250.
%t A276092 Table[Product[Prime[i]^(Prime[i] - 1), {i, n}], {n, 0, 9}] (* _Michael De Vlieger_, Aug 31 2016 *)
%o A276092 (Scheme)
%o A276092 (define (A276092 n) (let outloop ((i n) (t 1)) (if (zero? i) t (let ((p (A000040 i))) (let inloop ((j (- p 1)) (t t)) (if (zero? j) (outloop (- i 1) t) (inloop (- j 1) (* t p))))))))
%o A276092 ;; Or as a recurrence:
%o A276092 (definec (A276092 n) (if (zero? n) 1 (* (A276092 (- n 1)) (expt (A000040 n) (- (A000040 n) 1)))))
%o A276092 (PARI)
%o A276092 A276092(n) = prod(i=1, n, prime(i)^(prime(i) - 1)) \\ _Rick L. Shepherd_, Aug 23 2016
%Y A276092 Cf. A000040, A002110, A057588, A036878, A276086.
%Y A276092 Subsequence of A048103.
%K A276092 nonn
%O A276092 0,2
%A A276092 _Antti Karttunen_, Aug 22 2016