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A267892 Numbers with 9 odd divisors. 8
225, 441, 450, 882, 900, 1089, 1225, 1521, 1764, 1800, 2178, 2450, 2601, 3025, 3042, 3249, 3528, 3600, 4225, 4356, 4761, 4900, 5202, 5929, 6050, 6084, 6498, 6561, 7056, 7200, 7225, 7569, 8281, 8450, 8649, 8712, 9025, 9522, 9800, 10404, 11858, 12100, 12168, 12321, 12996, 13122, 13225, 14112, 14161, 14400, 14450, 15129 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Positive integers that have exactly nine odd divisors.
Numbers n such that the symmetric representation of sigma(n) has 9 subparts. - Omar E. Pol, Dec 29 2016
From Robert Israel, Dec 29 2016: (Start)
Numbers n such that A000265(n) is in A030627.
Numbers of the form 2^j*p^8 or 2^j*p^2*q^2 where p and q are distinct odd primes. (End)
Numbers that can be formed in exactly 8 ways by summing sequences of 2 or more consecutive positive integers. - Julie Jones, Aug 13 2018
LINKS
FORMULA
A001227(a(n)) = 9.
MAPLE
N:= 10^5: # to get all terms <= N
P:= select(isprime, [seq(i, i=3..floor(sqrt(N)/2), 2)]);
Aodd:= select(`<=`, map(t -> t^8, P) union {seq(seq(P[i]^2*P[j]^2, i=1..j-1), j=1..nops(P))}, N):
A:= map(t -> seq(2^j*t, j=0..ilog2(N/t)), Aodd):
sort(convert(A, list)); # Robert Israel, Dec 29 2016
MATHEMATICA
Select[Range[5^6], Length[Divisors@ # /. d_ /; EvenQ@ d -> Nothing] == 9 &] (* Michael De Vlieger, Apr 04 2016 *)
Select[Range[16000], Total[Boole[OddQ[Divisors[#]]]]==9&] (* Harvey P. Dale, May 12 2019 *)
PROG
(PARI) isok(n) = sumdiv(n, d, (d%2)) == 9; \\ after Michel Marcus.
(GAP) A:=List([1..16000], n->DivisorsInt(n));; B:=List([1..Length(A)], i->Filtered(A[i], IsOddInt));;
a:=Filtered([1..Length(B)], i->Length(B[i])=9); # Muniru A Asiru, Aug 14 2018
CROSSREFS
Column 9 of A266531.
Numbers with exactly k odd divisors (k = 1..10): A000079, A038550, A072502, apparently A131651, A267696, A230577, A267697, A267891, this sequence, A267893.
Sequence in context: A207639 A077347 A207640 * A363217 A373087 A216419
KEYWORD
nonn
AUTHOR
Omar E. Pol, Apr 03 2016
STATUS
approved

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Last modified May 29 11:24 EDT 2024. Contains 372940 sequences. (Running on oeis4.)