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

1, 2, 18, 11250, 1323551250, 34329510752434301250, 799811863723341113907011901401250, 38919798565076223182552300534870824616780123359001250, 4052615498709835178737678586220586796222761283625319842830388618784835051250, 3679152532021669595137666762315244807517735994898621013565758767014111825486079213219685771368099483111250

Offset

0,2

Comments

Cumulative product of A036878 (after a(0)). - Rick L. Shepherd, Aug 23 2016

Links

Table of n, a(n) for n=0..9.

Formula

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

a(0) = 1; and for n >= 1, a(n) = a(n-1) * A000040(n)^(A000040(n)-1).

a(n) = A276086(A057588(n)).

Example

For n=0 we have an empty product, thus a(0) = 1.
For n=1, a(1) = 2^1.
For n=2, a(2) = 2^1 * 3^2 = 18.
For n=3, a(3) = 2^1 * 3^2 * 5^4 = 11250.

Mathematica

Table[Product[Prime[i]^(Prime[i] - 1), {i, n}], {n, 0, 9}] (* Michael De Vlieger, Aug 31 2016 *)

Prog

(Scheme)
(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))))))))
;; Or as a recurrence:
(definec (A276092 n) (if (zero? n) 1 (* (A276092 (- n 1)) (expt (A000040 n) (- (A000040 n) 1)))))
(PARI)
A276092(n) = prod(i=1, n, prime(i)^(prime(i) - 1)) \\ Rick L. Shepherd, Aug 23 2016

Crossrefs

Cf. A000040, A002110, A057588, A036878, A276086.

Subsequence of A048103.

Sequence in context: A059783 A309972 A208056 * A191554 A066361 A120929

Adjacent sequences: A276089 A276090 A276091 * A276093 A276094 A276095

Keyword

nonn

Author

Antti Karttunen, Aug 22 2016

Status

approved