

A243055


Difference between the indices of the smallest and the largest prime dividing n: If n = p_i * ... * p_k, where p_i <= ... <= p_k, where p_h = A000040(h), then a(n) = (ki), a(1) = 0 by convention.


16



0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 1, 0, 3, 1, 0, 0, 1, 0, 2, 2, 4, 0, 1, 0, 5, 0, 3, 0, 2, 0, 0, 3, 6, 1, 1, 0, 7, 4, 2, 0, 3, 0, 4, 1, 8, 0, 1, 0, 2, 5, 5, 0, 1, 2, 3, 6, 9, 0, 2, 0, 10, 2, 0, 3, 4, 0, 6, 7, 3, 0, 1, 0, 11, 1, 7, 1, 5, 0, 2, 0, 12, 0, 3, 4, 13, 8, 4, 0, 2
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OFFSET

1,10


COMMENTS

For n>=1, A100484(n+1) gives the position where n occurs for the first time (setting also the records for the sequence).
a(n) = the difference between the largest and the smallest parts of the partition having Heinz number n. We define the Heinz number of a partition p = [p_1, p_2, ..., p_r] as Product(p_jth prime, j=1...r) (concept used by Alois P. Heinz in A215366 as an "encoding" of a partition). For example, for the partition [1, 1, 2, 4, 10] we get 2*2*3*7*29 = 2436. Example: a(57) = 6; indeed, the partition having Heinz number 57 = 3*19 is [2, 8].  Emeric Deutsch, Jun 04 2015


LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10000
Index entries for sequences computed from indices in prime factorization


FORMULA

If n = p_i * ... * p_k, where p_i <= ... <= p_k are not necessarily distinct primes (sorted into nondescending order) in the prime factorization of n, where p_i = A000040(i), then a(n) = (ki).
a(n) = A061395(n)  A055396(n).


MAPLE

with(numtheory):
a:= n> `if`(n=1, 0, (f> pi(max(f[]))pi(min(f[])))(factorset(n))):
seq(a(n), n=1..100); # Alois P. Heinz, Jun 04 2015


MATHEMATICA

a[1]=0; a[n_] := Function[{f}, PrimePi[Max[f]]  PrimePi[Min[f]]][FactorInteger[n][[All, 1]]]; Table[a[n], {n, 1, 100}] (* JeanFrançois Alcover, Jul 29 2015, after Alois P. Heinz *)


PROG

(Scheme) (define (A243055 n) ( (A061395 n) (A055396 n)))


CROSSREFS

Differs from A242411 for the first time at n=30.
A000961 gives the positions of zeros.
Cf. A243056, A241917, A241919, A049084, A027748, A055396, A061395, A100484, A215366.
Sequence in context: A087073 A242411 A286470 * A245151 A243978 A106844
Adjacent sequences: A243052 A243053 A243054 * A243056 A243057 A243058


KEYWORD

nonn


AUTHOR

Antti Karttunen, May 31 2014


STATUS

approved



