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
Examples
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.
Links
- Rémy Sigrist, Table of n, a(n) for n = 0..8192
Programs
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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)) }
Comments