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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 (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 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: A025212 A024972 A048749 * A097889 A256874 A250121 Adjacent sequences:  A336902 A336903 A336904 * A336906 A336907 A336908 KEYWORD nonn AUTHOR Rémy Sigrist, Aug 07 2020 STATUS approved

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Last modified September 26 23:42 EDT 2021. Contains 347673 sequences. (Running on oeis4.)