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(i-j) (where prime(k) denotes the k-th prime number and the p-adic valuation of a number is the greatest m such that p^m divides that number).

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

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 2-adic valuation is in correspondence with the 5-adic valuation,
- the 11-adic valuation is in correspondence with the 13-adic valuation,
- the p-adic 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: A024972 A048749 A355527 * A097889 A256874 A250121

Adjacent sequences: A336902 A336903 A336904 * A336906 A336907 A336908

Keyword

nonn

Author

Rémy Sigrist, Aug 07 2020

Status

approved