A045965 a(1)=2; if n = Product p_i^e_i, n > 1, then a(n) = Product p_{i+1}^e_i.

2, 3, 5, 9, 7, 15, 11, 27, 25, 21, 13, 45, 17, 33, 35, 81, 19, 75, 23, 63, 55, 39, 29, 135, 49, 51, 125, 99, 31, 105, 37, 243, 65, 57, 77, 225, 41, 69, 85, 189, 43, 165, 47, 117, 175, 87, 53, 405, 121, 147, 95, 153, 59, 375, 91, 297, 115, 93, 61, 315, 67, 111, 275, 729, 119

Offset: 1

Author

N. J. A. Sloane

Keywords

• easy
• nonn
• nice

References

• From a puzzle proposed by Marc LeBrun.

Links

• Indranil Ghosh, Table of n, a(n) for n = 1, 10000

Crossrefs

Cf. A048673. Essentially identical to A003961.

Programs

Haskell

a045965 n = if n == 1 then 2 else a003961 n
-- Reinhard Zumkeller, Jul 12 2012

Maple

succfactorization := proc(n) local p,d; if(1 = n) then RETURN(2); fi; p := 1; for d in ifactors(n)[ 2 ] do p := p * (nextprime(d[ 1 ])^d[ 2 ]); od; RETURN(p); end;

Mathematica

a[1] = 2; a[p_?PrimeQ] := a[p] = Prime[PrimePi[p] + 1]; a[n_] := a[n] = Times @@ (a[First[#]]^Last[#] &) /@ FactorInteger[n]; Table[ a[n], {n, 1, 65}] (* Jean-François Alcover, Jul 18 2013 *)

PARI

a(n) = if (n==1, 2, my(f=factor(n)); for(i=1, #f~, f[i,1] = nextprime(f[i,1]+1)); factorback(f)); \\ Michel Marcus, May 18 2020

Python

from sympy import factorint, primepi, prime, prod
def a(n):
    f=factorint(n)
    return 2 if n==1 else prod(prime(primepi(i) + 1)**f[i] for i in f) # Indranil Ghosh, May 15 2017

Extensions

More terms from David W. Wilson