The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A097318 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A097318

Numbers with more than one prime factor and, in the ordered factorization, the exponent never increases when read from left to right.
(history; published version)

#22 by Alois P. Heinz at Mon Nov 11 10:50:22 EST 2019

STATUS

editing

approved

#21 by Alois P. Heinz at Mon Nov 11 10:50:20 EST 2019

LINKS

Alois P. Heinz, <a href="/A097318/b097318.txt">Table of n, a(n) for n = 1..20000</a>

#20 by Alois P. Heinz at Mon Nov 11 10:47:09 EST 2019

MAPLE

q:= n-> (l-> (t-> t>1 and andmap(i-> l[i, 2]>=l[i+1, 2],

[$1..t-1]))(nops(l)))(sort(ifactors(n)[2])):

select(q, [$1..120])[]; # Alois P. Heinz, Nov 11 2019

#19 by Alois P. Heinz at Mon Nov 11 10:36:45 EST 2019

COMMENTS

If n = prod_Product_{k=1..m} p(k)^e(k), then m > 1, e(1) >= e(2) >= ... >= e(m).

These are numbers whose ordered prime signature is weakly decreasing. Weakly increasing is A304678. Prime Ordered prime signature is A124010. - Gus Wiseman, Nov 10 2019

#18 by Alois P. Heinz at Mon Nov 11 10:35:21 EST 2019

COMMENTS

These are numbers whose ordered prime signature is weakly decreasing. Weakly increasing is A304678. Prime signature is A124010. - Gus Wiseman, Nov 10 2019

STATUS

proposed

editing

#17 by Gus Wiseman at Mon Nov 11 09:34:27 EST 2019

STATUS

editing

proposed

#16 by Gus Wiseman at Sun Nov 10 09:54:34 EST 2019

COMMENTS

These are numbers whose prime signature is weakly decreasing. Weakly increasing is A304678. Prime signature is A124010. - Gus Wiseman, Nov 10 2019

CROSSREFS

Cf. A001222, A025487, A118914, A124010, A304678, A329138, A329142.

STATUS

approved

editing

#15 by N. J. A. Sloane at Thu Jun 16 23:27:25 EDT 2016

LINKS

S. Ramanujan, <a href="http://www.imsc.res.in/~rao/ramanujan/CamUnivCpapers/Cpaper34/page1.htm">Asymptotic formulae formulas for the distribution of integers of various types</a>, Proc. London Math. Soc. 2, 16 (1917), 112-132.

Discussion

Thu Jun 16

23:27

OEIS Server: https://oeis.org/edit/global/2523

#14 by Bruno Berselli at Thu Mar 12 07:26:42 EDT 2015

STATUS

proposed

approved

#13 by Colin Barker at Thu Mar 12 06:57:08 EDT 2015

STATUS

editing

proposed