A285639 a(n) = n*A117366(n)/spf(n), where A117366(n) is the smallest prime larger than all prime factors of n, and spf is the smallest prime factor of n (or 1 if n = 1).

2, 3, 5, 6, 7, 15, 11, 12, 15, 35, 13, 30, 17, 77, 35, 24, 19, 45, 23, 70, 77, 143, 29, 60, 35, 221, 45, 154, 31, 105, 37, 48, 143, 323, 77, 90, 41, 437, 221, 140, 43, 231, 47, 286, 105, 667, 53, 120, 77, 175, 323, 442, 59, 135, 143, 308, 437, 899, 61, 210, 67, 1147

Offset: 1

Author

M. F. Hasler, Apr 30 2017

Keywords

• nonn

Comments

The smallest prime factor of n is removed, and a prime factor larger than all others is added. This is somewhat in the spirit of A003961 where each of the prime factors is increased to the next larger prime. Therefore a(n) = A003961(n) when n is a prime or a product of consecutive primes.

Leaves invariant A073485, i.e., for all n in A073485, a(n) is again in A073485. More precisely, a(A098012(m,n)) = A098012(m,n+1). - M. F. Hasler, May 03 2017

Examples

			a(1) = nextprime(1) = 2.
a(2) = 2 / 2 * nextprime(2) = 3.
a(3) = 3 / 3 * nextprime(3) = 5, and in the same way, a(prime(k))=prime(k+1).
a(4) = 4 / 2 * nextprime(2) = 2*3 = 6.
a(6) = 6 / 2 * nextprime(3) = 3*5 = 15.
		

Links

• Ivan Neretin, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A020639, A003961, A006530, A117366, A151800.

Programs

Mathematica

Table[d = FactorInteger[n]; n*NextPrime[d[[-1, 1]]]/d[[1, 1]], {n, 62}] (* Ivan Neretin, Jan 23 2018 *)

PARI

a(n,f=factor(n)[,1])={f||f=[1];n\f[1]*nextprime(f[#f]+1)}