A370205 Numbers j whose symmetric representation of sigma(j) consists of the single unimodal width pattern 121.

6, 12, 20, 24, 28, 40, 48, 56, 80, 88, 96, 104, 112, 160, 176, 192, 208, 224, 272, 304, 320, 352, 368, 384, 416, 448, 464, 496, 544, 608, 640, 704, 736, 768, 832, 896, 928, 992, 1088, 1184, 1216, 1280, 1312, 1376, 1408, 1472, 1504, 1536, 1664, 1696, 1792, 1856, 1888, 1952, 1984

Offset

1,1

Comments

Every term has 2 odd divisors and has the form 2^k * p, k > 0, p prime and 2 < p < 2^(k+1), and therefore is a subsequence of A082662. The two 1's in row a(n) of the triangle of A237048 occur in positions 1 and p up to the diagonal since p <= floor( (sqrt(8*a(n) + 1) - 1)/2 ) < 2^(k+1) which represents the unimodal width pattern 121 in SRS(a(n)).

Numbers in this sequence divisible by 5 have the form 2^(k+2) * 5, k >= 0, the least being a(3) = 20.

Links

Table of n, a(n) for n=1..55.

Mathematica

(* function based on conditions for the odd divisors - fast computation *)
a370205Q[n_] := Module[{p=NestWhile[#/2&, n, EvenQ[#]&]}, PrimeQ[p]&&p^2<2n)]
a370205[m_, n_] := Select[Range[m, n], a370205Q]
a370205[1, 1984]
(* widthPattern[ ] and support functions are defined in A341969 - slow computation *)
a370205[m_, n_] := Select[Range[m, n], widthPattern[#]=={1, 2, 1}&]
a370205[1, 1984]

Crossrefs

Cf. A082662, A235791, A237048, A237270, A237271, A237591, A237593, A249223, A262045, A341969, A342592, A342594, A342595, A342596.

Sequence in context: A083207 A378541 A378599 * A304391 A145278 A094371

Adjacent sequences: A370202 A370203 A370204 * A370206 A370207 A370208

Keyword

nonn

Author

Hartmut F. W. Hoft, Feb 11 2024

Status

approved