A344530 For any number n with binary expansion Sum_{k = 1..m} 2^e_k (where 0 <= e_1 < ... < e_m), a(n) = Product_{k = 1..m} prime(1+e_k)^k (where prime(k) denotes the k-th prime number).

1, 2, 3, 18, 5, 50, 75, 2250, 7, 98, 147, 6174, 245, 17150, 25725, 5402250, 11, 242, 363, 23958, 605, 66550, 99825, 32942250, 847, 130438, 195657, 90393534, 326095, 251093150, 376639725, 870037764750, 13, 338, 507, 39546, 845, 109850, 164775, 64262250, 1183

Offset

0,2

Comments

All terms are distinct and belong to A304678.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..8192

Formula

a(0) = 1.

a(2*n) = A003961(a(n)).

a(2*n + 1) = A045967(a(n)).

a(2^n) = prime(n+1) for any n >= 0.

a(2^n - 1) = A076954(n) for any n >= 0.

Example

For n = 42:
- 42 = 2^1 + 2^3 + 2^5,
- a(42) = prime(1+1) * prime(1+3)^2 * prime(1+5)^3,
- a(42) = 3 * 7^2 * 13^3 = 322959.

Prog

(PARI) a(n) = { my (v=1, e); for (k=1, oo, if (n==0, return (v), n-=2^e=valuation(n, 2); v*=prime(1+e)^k)) }

Crossrefs

Cf. A003961, A045967, A076954, A304678.

Sequence in context: A130226 A287621 A348279 * A328624 A328627 A032808

Adjacent sequences: A344527 A344528 A344529 * A344531 A344532 A344533

Keyword

nonn,base

Author

Rémy Sigrist, May 22 2021

Status

approved