A133811 Numbers that are primally tight and have strictly ascending powers.

1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 18, 19, 23, 25, 27, 29, 31, 32, 37, 41, 43, 47, 49, 53, 54, 59, 61, 64, 67, 71, 73, 75, 79, 81, 83, 89, 97, 101, 103, 107, 108, 109, 113, 121, 125, 127, 128, 131, 137, 139, 149, 151, 157, 162, 163, 167, 169, 173, 179, 181, 191

Offset

1,2

Comments

All numbers of the form p_1^k1*p_2^k2*...*p_n^k_n, where k1 < k2 < ... < k_n and the p_i are n successive primes.

Subset of A073491, A133810.

Different from A082377 starting n=16.

Different from A000961 (prime powers) starting n=13.

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Prog

(Haskell)
a133811 n = a133811_list !! (n-1)
a133811_list = 1 : filter f [2..] where
   f x = (and $ zipWith (<) eps $ tail eps) &&
         (all (== 1) $ zipWith (-) (tail ips) ips)
     where ips = map a049084 $ a027748_row x
           eps = a124010_row x
-- Reinhard Zumkeller, Nov 07 2012
(PARI) isok(n) = {my(f = factor(n)); my(nbf = #f~); my(lastp = 0); for (i=1, nbf, if (lastp && (f[i, 1] != nextprime(lastp+1)), return (0)); lastp = f[i, 1]; ); for (j=2, nbf, if (f[j, 2] <= f[j-1, 2], return (0)); ); return (1); } \\ Michel Marcus, Jun 04 2014

Crossrefs

Cf. A025487, A087980, A073491, A133808-A133813.

Cf. A124010, A027748, A049084.

Sequence in context: A362616 A334965 A362621 * A316525 A119314 A317923

Adjacent sequences: A133808 A133809 A133810 * A133812 A133813 A133814

Keyword

nonn

Author

Olivier Gérard, Sep 23 2007

Status

approved