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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).
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
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.
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
Sequence in context: A024972 A048749 A355527 * A097889 A256874 A250121
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Aug 07 2020
STATUS
approved