A389230 Even numbers k whose symmetric representation of sigma, SRS(k), consists of an odd number, >1, of parts and whose center part is the minimum of all parts.

50, 70, 98, 110, 130, 154, 170, 182, 190, 238, 242, 266, 286, 322, 338, 350, 374, 418, 442, 484, 494, 506, 550, 572, 578, 598, 638, 646, 650, 676, 682, 722, 748, 754, 770, 782, 806, 814, 836, 850, 874, 884, 902, 910, 946, 950, 962, 986, 988, 1012, 1014, 1054, 1058, 1066

Offset

1,1

Comments

All numbers of the form k = 2^s * p^(2*m), s, m >= 1 and p prime satisfying 2^(s+1) < p, belong to this sequence; for these numbers k, SRS(k) has maximum width 1, consists of 2*m+1 parts and its center part has size (2^(s+1) - 1) * p^m; except for 8 and 18, A079704 and A143928 are subsequences of these numbers.

Links

Table of n, a(n) for n=1..54.

Example

a(1) = 50 is the smallest even number whose symmetric representation of sigma consists of more than two parts and SRS(50) = {39, 15, 39}.
a(2) = 70 is the smallest number whose center part of SRS(70) = {54, 36, 74} divides sigma(70) = 144 = 4*36.
a(51) = 1014 = 2*3*13^2 is the smallest number in the sequence for which its first part of the symmetric representation of sigma has maximum width larger than 1; its width pattern is 1 2 1 0 1 2 1 0 1 2 1.
3850 is the smallest even number whose symmetric representation of sigma consists of at least 3 parts that does not belong to the sequence since SRS(3850) = {2889, 3150, 2889}.

Mathematica

(* Function partsSRS[ ] is defined in A377654 *)
a389230Q[n_] := Module[{ps=partsSRS[n], len}, len=Length[ps]; EvenQ[n]&& OddQ[len]&&len>2&&ps[[(len+1)/2]]==Min[ps]]
a389230[n_] := Select[Range[n], a389230Q]
a389230[1066]

Crossrefs

Cf. A003056, A079704, A143928, A235791, A237048, A237591, A237593, A249223, A377654.

Sequence in context: A380871 A224559 A272607 * A224552 A039473 A309123

Adjacent sequences: A389227 A389228 A389229 * A389231 A389232 A389233

Keyword

nonn

Author

Hartmut F. W. Hoft, Oct 28 2025

Status

approved