The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A330975 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A330975

Numbers that are not the number of factorizations of n into distinct factors > 1 for any n.
(history; published version)

#11 by M. F. Hasler at Sun Jan 26 20:42:45 EST 2020

STATUS

reviewed

approved

#10 by Joerg Arndt at Sun Jan 26 01:46:57 EST 2020

STATUS

proposed

reviewed

Discussion

Sun Jan 26

20:42

M. F. Hasler: Thanks for  the additional xref. (Would be good to add hints on what the A-numbers refer to...:-)

#9 by David A. Corneth at Sat Jan 25 11:30:41 EST 2020

STATUS

editing

proposed

#8 by David A. Corneth at Wed Jan 08 10:09:50 EST 2020

CROSSREFS

Cf. A001222, A002033, A025487, A033833, A045780, A045783, A318286, A328966, A330972, A330973, A330997.

STATUS

approved

editing

Discussion

Wed Jan 22

12:56

OEIS Server: This sequence has not been edited or commented on for a week
yet is not proposed for review.  If it is ready for review, please
visit https://oeis.org/draft/A330975 and click the button that reads
"These changes are ready for review by an OEIS Editor."

Thanks.
  - The OEIS Server

#7 by Susanna Cuyler at Wed Jan 08 09:44:55 EST 2020

STATUS

proposed

approved

#6 by Gus Wiseman at Wed Jan 08 02:47:28 EST 2020

STATUS

editing

proposed

#5 by Gus Wiseman at Wed Jan 08 02:39:28 EST 2020

CROSSREFS

Strict factorizations are A045778, with image A045779, with complement A330975.

#4 by Gus Wiseman at Wed Jan 08 02:38:54 EST 2020

CROSSREFS

Factorizations are A001055, with image A045782, with complement A330976.

Strict factorizations are A045778, with image A045779, with complement A330975.

The least positive integer with exactly n strict factorizations is A330974(n).

#3 by Gus Wiseman at Tue Jan 07 16:06:19 EST 2020

CROSSREFS

The least positive integer with exactly n strict factorizations is A330974(n).

#2 by Gus Wiseman at Tue Jan 07 15:46:06 EST 2020

NAME

allocated Numbers that are not the number of factorizations of n into distinct factors > 1 for Gus Wisemanany n.

DATA

11, 13, 20, 23, 24, 26, 28, 29, 30, 35, 36, 37, 39, 41, 45, 47, 48, 49, 50, 51, 53, 58, 60, 62, 63, 65, 66, 68, 69, 71, 72, 73, 75, 77, 78, 79, 81, 82, 84, 85, 86, 87, 90, 92, 94, 95, 96, 97, 98, 99, 101, 102, 103, 105, 106, 107, 108, 109, 113, 114, 115, 118

OFFSET

1,1

COMMENTS

Warning: I have only confirmed the first three terms. The rest are derived from A045779. - Gus Wiseman, Jan 07 2020

LINKS

R. E. Canfield, P. Erdős and C. Pomerance, <a href="http://math.dartmouth.edu/~carlp/PDF/paper39.pdf">On a Problem of Oppenheim concerning "Factorisatio Numerorum"</a>, J. Number Theory 17 (1983), 1-28.

MATHEMATICA

nn=20;

fam[n_]:=fam[n]=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[fam[n/d], Min@@#>=d&]], {d, Rest[Divisors[n]]}]];

nds=Length/@Array[Select[fam[#], UnsameQ@@#&]&, 2^nn];

Complement[Range[nn], nds]

CROSSREFS

Complement of A045779.

The non-strict version is A330976.

Factorizations are A001055, with image A045782.

Strict factorizations are A045778, with image A045779.

The least positive integer with exactly n strict factorizations is A330974.

Cf. A001222, A002033, A033833, A045780, A045783, A318286, A328966, A330972, A330973, A330997.

KEYWORD

allocated

nonn

AUTHOR

Gus Wiseman, Jan 07 2020

STATUS

approved

editing