OFFSET
1,2
COMMENTS
Old name was: "If the prime factorization of n is n=product{p|n} p^b(n,p), then a(n) = the smallest positive integer such that each p^b(n,p) divides a different integer k where a(n) <= k <= a(n)+{number distinct prime divisors of n}-1. a(1)=1."
Clarification of definition: Each b(n,p) is a positive integer. Let the number of distinct primes dividing n be P. There is a permutation (c(1),c(2),c(3),...c(P)) of the p^b(n,p)'s such that c(1)|a(n), c(2)|(a(n)+1), c(3)|(a(n)+2),..., c(P)|(a(n)+P-1).
LINKS
Charlie Neder, Table of n, a(n) for n = 1..1000
FORMULA
a(n) = n iff n is a prime power (A000961). - Charlie Neder, Feb 03 2019
EXAMPLE
3150 is factored as 2^1 * 3^2 * 5^2 * 7^1. a(3150) = 25, which can be seen from 5^2|25, 2^1|26, 3^2|27, and 7^1|28.
PROG
(PARI) isokp(m, perm, f, nb) = {for (k=1, nb, if ((m+k-1) % f[perm[k], 1]^f[perm[k], 2], return (0)); ); return (1); }
isokm(m, f, nb) = {for (j=0, nb!-1, my(perm = numtoperm(nb, j)); if (isokp(m, perm, f, nb), return (1)); ); return (0); }
a(n) = {my(f = factor(n), nb = #f~, m = 1); while (! isokm(m, f, nb), m++); m; } \\ Michel Marcus, Feb 05 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Leroy Quet, Jul 19 2009
EXTENSIONS
Name changed and a(31)-a(72) by Charlie Neder, Feb 03 2019
STATUS
approved