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

1,1

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

Links

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

Example

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.

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A103538 A144671 A073721 * A090745 A002229 A299158

Adjacent sequences: A285636 A285637 A285638 * A285640 A285641 A285642

Keyword

nonn

Author

M. F. Hasler, Apr 30 2017

Status

approved