A319354 a(n) = Product prime(k), where k ranges over the lengths of all arithmetic progressions formed from the divisors of n (with at least two distinct terms each); a(1) = 2 by convention.

2, 3, 3, 27, 3, 1215, 3, 729, 27, 729, 3, 93002175, 3, 729, 1215, 59049, 3, 39858075, 3, 14348907, 729, 729, 3, 576626970315375, 27, 729, 729, 23914845, 3, 176518460300625, 3, 14348907, 729, 729, 729, 6305415920398625625, 3, 729, 729, 38127987424935, 3, 63546645708225, 3, 14348907, 66430125, 729, 3, 289588836976147679079375, 27, 14348907, 729

Offset

1,1

Links

Antti Karttunen, Table of n, a(n) for n = 1..4096

Formula

For all n >= 1:

A061395(a(n)) = A067131(n).

A071178(a(n)) = A160752(n).

For all n >= 2, A001222(a(n)) = A066446(n).

Example

For n = 6, the arithmetic progressions found in its divisor set {1, 2, 3, 6} are: {1, 2}, {1, 3}, {2, 3}, {2, 6}, {3, 6} and {1, 2, 3}. Five of these have length 2, and one is of length 3, thus a(6) = prime(2)^5 * prime(3) = 243*5 = 1215.

Prog

(PARI) A319354(n) = if(1==n, 2, my(d=divisors(n), m=1); for(i=1, (#d-1), for(j=(i+1), #d, my(c=1, k=d[j], s=(d[j]-d[i])); while(!(n%k), k+=s; c++); m *= prime(c))); (m));

Crossrefs

Cf. A319355 (rgs-transform).

Sequence in context: A084956 A216724 A281786 * A100650 A096502 A101462

Adjacent sequences: A319351 A319352 A319353 * A319355 A319356 A319357

Keyword

nonn

Author

Antti Karttunen, Sep 21 2018

Status

approved