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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
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
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
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, May 22 2021
STATUS
approved