A335049 The prime factorization of a(n) corresponds to the left diagonal of the XOR-triangle built from prime factorization of n, with 2-adic valuation of a(n) given by last row.
1, 2, 6, 4, 30, 3, 210, 8, 36, 15, 2310, 24, 30030, 105, 10, 16, 510510, 72, 9699690, 120, 35, 1155, 223092870, 12, 900, 15015, 216, 840, 6469693230, 5, 200560490130, 32, 770, 255255, 21, 9, 7420738134810, 4849845, 5005, 60, 304250263527210, 70
Offset: 1
Examples
For n = 198:
- 198 = 11^1 * 7^0 * 5^0 * 3^2 * 2^1,
- the corresponding XOR-triangle is:
1 0 0 2 1
1 0 2 3
1 2 1
3 3
0
- so a(n) = 11^1 * 7^1 * 5^1 * 3^3 * 2^0 = 10395.
Links
Programs
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PARI
a(n) = { my (f=factor(n), m=if (#f~==0, 0, primepi(f[#f~, 1])), x=vector(m, k, valuation(n, prime(m+1-k))), v=1); forstep (i=m, 1, -1, v*=prime(i)^x[1]; x=vector(#x-1, k, bitxor(x[k], x[k+1])); ); v }
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