A034684 If n = p_1^e_1 * ... * p_k^e_k, p_1 < ... < p_k primes, then a(n) = min { p_i^e_i }.

1, 2, 3, 4, 5, 2, 7, 8, 9, 2, 11, 3, 13, 2, 3, 16, 17, 2, 19, 4, 3, 2, 23, 3, 25, 2, 27, 4, 29, 2, 31, 32, 3, 2, 5, 4, 37, 2, 3, 5, 41, 2, 43, 4, 5, 2, 47, 3, 49, 2, 3, 4, 53, 2, 5, 7, 3, 2, 59, 3, 61, 2, 7, 64, 5, 2, 67, 4, 3, 2, 71, 8, 73, 2, 3, 4, 7, 2, 79, 5, 81, 2, 83, 3, 5, 2, 3, 8, 89, 2, 7, 4

Offset: 1

Author

Erich Friedman

Keywords

• nonn
• nice
• easy

Comments

a(1) = 1; for n > 1, smallest unitary divisor of n that is larger than 1.

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A020639, A006530, A034684, A028233, A034699, A053585.

Cf. A034444, A034448, A052125.

Cf. A001221, A008475, A141809.

Programs

Haskell

a034684 = minimum . a141809_row  -- Reinhard Zumkeller, Jan 29 2013

Mathematica

A034684[n_]:=Min[(#[[1]]^#[[2]])&/@FactorInteger[n]]; Array[A034684,100] (* Enrique Pérez Herrero, Nov 01 2011 *)

PARI

A034684(n) = {local(f,m);if(n==1,1,f=factor(n);m=f[1,1]^f[1,2];for(i=1,matsize(f)[1],m=min(m,f[i,1]^f[i,2]));m)} \\ Michael B. Porter, Jan 28 2010

Formula

a(n) = min{A141809(n,k): k=1..A001221(n)}. - Reinhard Zumkeller, Jan 29 2013

a(n) = n/A052125(n). - Amiram Eldar, Sep 16 2024