A318954 Minimum shifted Heinz number of a strict factorization of n into factors > 1.

1, 2, 3, 5, 7, 6, 13, 10, 19, 14, 29, 15, 37, 26, 21, 34, 53, 33, 61, 35, 39, 58, 79, 30, 89, 74, 57, 65, 107, 42, 113, 85, 87, 106, 91, 66, 151, 122, 111, 70, 173, 78, 181, 145, 129, 158, 199, 102, 223, 161, 159, 185, 239, 114, 203, 130, 183, 214, 271, 105

Offset

1,2

Comments

The shifted Heinz number of a factorization (y_1, ..., y_k) is prime(y_1 - 1) * ... * prime(y_k - 1).

Links

Table of n, a(n) for n=1..60.

Example

The strict factorizations of 60 are (2*3*10), (2*5*6), (2*30), (3*4*5), (3*20), (4*15), (5*12), (6*10), (60), with shifted Heinz numbers 138, 154, 218, 105, 201, 215, 217, 253, 277 respectively, so a(60) = 105.

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)&/@Select[facs[n], UnsameQ@@#&]], {n, 100}]

Crossrefs

Cf. A001055, A007716, A045778, A056239, A080688, A162247, A215366, A246868, A318871, A318953.

Sequence in context: A338224 A355701 A353955 * A296375 A306923 A366856

Adjacent sequences: A318951 A318952 A318953 * A318955 A318956 A318957

Keyword

nonn

Author

Gus Wiseman, Sep 05 2018

Status

approved