A064554 a(n) = Min {k | A064553(k) = n}.

1, 2, 3, 4, 7, 6, 13, 8, 9, 14, 29, 12, 37, 26, 21, 16, 53, 18, 61, 28, 39, 58, 79, 24, 49, 74, 27, 52, 107, 42, 113, 32, 87, 106, 91, 36, 151, 122, 111, 56, 173, 78, 181, 116, 63, 158, 199, 48, 169, 98, 159, 148, 239, 54, 203, 104, 183, 214, 271, 84, 281, 226, 117, 64

Offset: 1

Author

Reinhard Zumkeller, Sep 21 2001

Keywords

• nonn

Comments

A064553(a(n)) = n and A064553(a(k)) <> k for k < a(n). For prime p, a(p)=prime(p-1), which is sequence A055003. - T. D. Noe, Dec 12 2004

a(n) is not multiplicative because a(7*13) = a(91) = 463, but a(7)*a(13) = 13*37 = 481 and 91 is the smallest possible such n. - Christian G. Bower, May 19 2005

a(n) = A080688(n,1). - Reinhard Zumkeller, Oct 01 2012

Minimal shifted Heinz number of a factorization of n, where the shifted Heinz number of a factorization (y_1, ..., y_k) is prime(y_1 - 1) * ... * prime(y_k - 1). - Gus Wiseman, Sep 05 2018

Links

• T. D. Noe, Table of n, a(n) for n = 1..8000
• T. D. Noe, Plot of A064554

Crossrefs

Cf. A064555, A001055, A064553.

Cf. A055003 (prime(prime(n)-1)).

Cf. A007716, A056239, A162247, A215366, A246868, A318871.

Programs

Haskell

a064554 = head . a080688_row  -- Reinhard Zumkeller, Oct 01 2012

Mathematica

facs[n_]:=If[n<=1,{{}},Join@@Table[(Prepend[#1,d]&)/@Select[facs[n/d],Min@@#1>=d&],{d,Rest[Divisors[n]]}]];
Table[Min[Times@@Prime/@(#-1)&/@facs[n]],{n,100}] (* Gus Wiseman, Sep 05 2018 *)