A318885 If n = p^a * q^b * ... * r^c, with p < q < r primes, with nonzero exponents a, b, c, then a(n) = prime(1+p-p)^a * prime(1+q-p)^b * ... * prime(1+r-p)^c; a(1) = 1.

1, 2, 2, 4, 2, 6, 2, 8, 4, 14, 2, 12, 2, 26, 10, 16, 2, 18, 2, 28, 22, 58, 2, 24, 4, 74, 8, 52, 2, 42, 2, 32, 46, 106, 10, 36, 2, 122, 62, 56, 2, 78, 2, 116, 20, 158, 2, 48, 4, 98, 94, 148, 2, 54, 34, 104, 118, 214, 2, 84, 2, 226, 44, 64, 46, 174, 2, 212, 146, 182, 2, 72, 2, 302, 50, 244, 22, 222, 2, 112, 16, 346, 2, 156, 82, 362, 206, 232, 2

Offset: 1

Author

Antti Karttunen, Sep 24 2018

Keywords

• nonn

Examples

			For n = 10 = 2^1 * 5^1, a(n) = prime(1)^1 * prime(1+5-2)^1 = prime(1) * prime(4) = 2*7 = 14.
For n = 55 = 5^1 * 11^1, a(n) = prime(1)^1 * prime(1+11-5)^1 = prime(1) * prime(7) = 2*17 = 34.
For n = 90 = 2^1 * 3^2 * 5^1, a(n) = prime(1)^1 * prime(1+3-2)^2 * prime(1+5-2)^1 = 2^1 * 3^2 * 7^1 = 126.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384

Crossrefs

Cf. A318887 (rgs-transform), A318888.

Programs

PARI

A318885(n) = if(1==n,n,my(f=factor(n),m=2^f[1,2],i=1); for(k=2,#f~,i += (f[k,1]-f[k-1,1]); m *= prime(i)^f[k,2]); (m));