

A336905


Numbers n such that for any i > 0 there is some j > 0 such that the prime(i)adic valuation of n, say x, equals the prime(j)adic valuation of n and x = abs(ij) (where prime(k) denotes the kth prime number and the padic valuation of a number is the greatest m such that p^m divides that number).


0



1, 6, 15, 30, 35, 77, 100, 105, 143, 210, 221, 323, 385, 437, 441, 462, 667, 858, 899, 1001, 1147, 1155, 1326, 1517, 1763, 1938, 2021, 2145, 2310, 2431, 2491, 2622, 2744, 3025, 3127, 3315, 3599, 4002, 4087, 4199, 4290, 4757, 4845, 5005, 5183, 5394, 5767, 6006
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

This sequence has connections with A336880.
All products of two successive prime numbers (A006094) belong to this sequence.
The product of two terms that are coprime is also a term.


LINKS

Table of n, a(n) for n=1..48.


EXAMPLE

Regarding 14300:
 14300 = 2^2 * 5^2 * 11 * 13 = prime(1)^2 * prime(3)^2 * prime(5) * prime(6),
 the 2adic valuation is in correspondence with the 5adic valuation,
 the 11adic valuation is in correspondence with the 13adic valuation,
 the padic valuation is in correspondence with itself for any prime number p that does not divide 14300,
 so 14300 is a term.


PROG

(PARI) is(n) = { my (f=factor(n), x=f[, 2]~, pi=apply(primepi, f[, 1]~), u, v); for (k=1, #x, if (((u=setsearch(pi, pi[k]x[k])) && x[u]==x[k])  ((v=setsearch(pi, pi[k]+x[k])) && x[v]==x[k]), "OK", return (0))); return (1) }


CROSSREFS

Cf. A006094, A336880.
Sequence in context: A025212 A024972 A048749 * A097889 A256874 A250121
Adjacent sequences: A336902 A336903 A336904 * A336906 A336907 A336908


KEYWORD

nonn


AUTHOR

Rémy Sigrist, Aug 07 2020


STATUS

approved



