A075047 -id:A075047 - cp's OEIS frontend

A025283 Composites that use the same digits as their prime factorization.

25, 121, 1255, 2349, 5120, 12337, 12955, 17482, 25105, 41323, 43375, 93217, 100255, 101299, 105295, 107329, 117067, 124483, 127417, 129595, 132565, 145273, 146137, 149782, 163797, 174082, 174298, 174793, 174982, 191239, 250105, 256315, 263155

Offset: 1

David W. Wilson

Here exponents equal to 1 are not taken into account, so 1255 = 5^1*251^1 = 5*251 is a term. Prime numbers are excluded because they all trivially use the same digits as their prime factorization. If, on the contrary, exponents equal to 1 are counted, the resulting sequence is A075047. - Giovanni Resta, Jul 14 2015

An interesting example of the factorization digits appearing in the same order as in its composite generator: 13532385396179 = 13 * 53^2 * 3853 * 96179. - Hans Havermann, Jun 28 2017

Giovanni Resta, Table of n, a(n) for n = 1..10000

Cf. A075047, A260046, A260047, A260048, A260049, A260050, A260051, A260052, A260053, A260054, A260055.

Select[Range[10^5], !PrimeQ@ # && Sort@ IntegerDigits@ # == Sort@ Flatten@ IntegerDigits@ Select[ Flatten@ FactorInteger@ #, #>1 &] &] (* Giovanni Resta, Jul 14 2015 *)

A075046 a(n) = the smallest number k such that the number of divisors of the n numbers from k through k+n-1 are in nondescending order.

Original entry on oeis.org

1, 1, 1, 1, 241, 241, 12853, 12853, 234613, 376741, 78312721, 125938261, 4019167441, 16586155153, 35237422882, 1296230533473, 42301168491121, 61118966262061

Offset: 1

Amarnath Murthy, Sep 03 2002

tau(k) <= tau(k+1) <= ... <= tau(k+n-1).
a(16) > 10^12. - Donovan Johnson, Oct 13 2009
a(17) > 10^13. - Giovanni Resta, Apr 12 2017
a(19) > 2.64*10^15. - Jud McCranie, Mar 27 2019
If a(n) > 1, then A013632(a(n)) >= n. Might be useful to help speed up brute force search. - Chai Wah Wu, May 04 2017

			a(5) = 241 = a(6) as tau(241) = 2 < tau(242) = tau(243) = tau(244) = tau(245) = 6 < tau(246).

Cf. A075028, A075029, A075031, A045983, A006073, A075044, A055927, A075047.

k = 1; Do[ While[t = Table[ DivisorSigma[0, i], {i, k, k + n - 1}]; t != Sort[t], k++ ]; Print[k], {n, 1, 11}]

More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 19 2003
a(11) from Robert G. Wilson v, Sep 07 2003
a(12)-a(15) from Donovan Johnson, Oct 13 2009
a(16) from Fred Schneider, Mar 29 2017
a(17)-a(18) from Jud McCranie, Mar 27 2019

cp's OEIS Frontend

A025283 Composites that use the same digits as their prime factorization.

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