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 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. 4
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified September 15 02:16 EDT 2024. Contains 375929 sequences. (Running on oeis4.)