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A248175 Least positive integer m such that m + n divides q(m*n), where q(.) is the strict partition function given by A000009. 2
11, 4, 9, 2, 12, 10, 9, 16, 3, 6, 1, 5, 2, 18, 7, 8, 5, 14, 11, 36, 2, 34, 4, 8, 31, 6, 15, 36, 23, 2, 9, 14, 17, 22, 11, 18, 1, 22, 11, 7, 1, 22, 12, 7, 55, 7, 19, 40, 15, 6, 31, 12, 43, 10, 25, 40, 7, 91, 61, 20 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Conjecture: (i) a(n) exists for any n > 0.
(ii) For each n > 0, there is a positive integer m such that m + n divides q(m) + q(n).
LINKS
EXAMPLE
a(3) = 9 since 9 + 3 = 12 divides q(9*3) = 192 = 12*16.
MATHEMATICA
Do[m=1; Label[aa]; If[Mod[PartitionsQ[m*n], m+n]==0, Print[n, " ", m]; Goto[bb]]; m=m+1; Goto[aa]; Label[bb]; Continue, {n, 1, 60}]
CROSSREFS
Sequence in context: A352162 A010187 A372761 * A114267 A166205 A141240
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, Oct 03 2014
STATUS
approved

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Last modified June 23 10:38 EDT 2024. Contains 373643 sequences. (Running on oeis4.)