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A296509 a(n) = (maximal size of partitions of n into distinct parts) minus (number of partitions of n into consecutive parts). 0
0, 0, 0, 0, 1, 0, 1, 1, 2, 0, 2, 2, 2, 2, 2, 1, 4, 3, 2, 3, 3, 2, 4, 4, 4, 3, 4, 2, 5, 5, 3, 5, 6, 3, 5, 3, 5, 6, 6, 4, 6, 6, 4, 6, 6, 3, 7, 7, 7, 6, 6, 5, 7, 7, 5, 6, 8, 6, 8, 8, 6, 8, 8, 4, 9, 6, 7, 9, 9, 7, 7, 9, 8, 9, 9, 5, 9, 7, 8, 10, 10, 7, 10, 10, 8, 8, 10, 8, 10, 10, 6, 9, 11, 9, 11, 9, 11, 11, 10, 7, 10, 11, 9 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,9

COMMENTS

Is this the same as A238005?

The trivial partitions of length 1 are included.

For n >= 1; a(n) is also the number of zeros in the n-th row of the triangles A196020, A211343, A231345, A236106, A237048, A239662, A261699, A271344, A272026, A280850, A285574, A285891, A285914, A286013, A296508 (and possibly more).

LINKS

Table of n, a(n) for n=0..102.

FORMULA

a(n) = A003056(n) - A001227(n), n >= 1; a(0) = 0.

MATHEMATICA

{0}~Join~Array[Floor[(Sqrt[1 + 8 #] - 1)/2] - DivisorSum[#, 1 &, OddQ] &, 102] (* Michael De Vlieger, Feb 18 2018 *)

PROG

(PARI) a(n) = if (n, (sqrtint(8*n+1)-1)\2 - sumdiv(n, d, d%2), 0); \\ Michel Marcus, Mar 01 2018

CROSSREFS

Cf. A286000 and A286001 (tables of partitions into consecutive parts).

Cf. A000009, A001227, A003056, A196020, A211343, A231345, A237048, A235791, A236106, A237591, A237593, A238005, A239662, A261699, A271344, A272026, A280850, A285574, A285891, A285914, A286013, A296508.

Sequence in context: A044944 A044945 A238005 * A089582 A044946 A044947

Adjacent sequences:  A296506 A296507 A296508 * A296510 A296511 A296512

KEYWORD

nonn

AUTHOR

Omar E. Pol, Feb 17 2018

STATUS

approved

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Last modified February 22 12:42 EST 2020. Contains 332136 sequences. (Running on oeis4.)