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 A370521 The smallest number k that can be partitioned in n ways as the sum of two Blum numbers (A016105). 1
 1, 42, 90, 162, 234, 474, 270, 378, 558, 594, 774, 846, 970, 810, 1050, 630, 1370, 1134, 990, 1170, 1470, 1730, 1530, 2054, 1970, 1386, 1638, 1710, 2178, 2070, 2630, 2250, 1890, 2730, 2394, 2310, 3234, 3230, 3530, 2790, 2898, 3650, 3470, 4010, 3570, 3654, 2970, 3150 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Michael S. Branicky, Table of n, a(n) for n = 0..11549 EXAMPLE 1 cannot be written as the sum of two Blum numbers, so a(0) = 1. Since A016105(k) >= 21, for k >= 1, the numbers 2 through 41 cannot be written as the sum of two Blum numbers. 42 = 21 + 21 = A016105(1) + A016105(1), so a(1) = 42. 90 = 21 + 69 = A016105(1) + A016105(4), 90 = 33 + 57 = A016105(2) + A016105(3), and the numbers 1 to 89 cannot be written in two ways as the sum of two Blum numbers. Thus a(2) = 90. PROG (Magma) pp:=PrimeDivisors; blum:=func; b:=[n: n in [1..5000]|blum(n)]; a:=[]; for n in [0..47] do k:=1; while #RestrictedPartitions(k, 2, Set(b)) ne n do k:=k+1; end while; Append(~a, k); end for; a; (Python) from sympy import factorint from itertools import takewhile from collections import Counter def okA016105(n): f = factorint(n) return len(f)==2 and sum(f.values())==2 and all(p%4==3 for p in f) def aupto(N): # N is limit of terms considered; use 2*10**6 for b-file s = [k for k in range(1, N+1) if okA016105(k)] c = Counter(x+y for i, x in enumerate(s) if 2*i<=N for y in s[i:] if x+y<=N) adict = {0: 1} for k in sorted(c): v = c[k] if v not in adict: adict[v] = k adict_rev = (adict.get(i) for i in range(max(adict)+1)) return list(takewhile(lambda v:v!=None, adict_rev)) print(aupto(4010)) # Michael S. Branicky, Feb 28 2024 CROSSREFS Cf. A016105. Sequence in context: A369275 A300603 A301328 * A067296 A044180 A044561 Adjacent sequences: A370518 A370519 A370520 * A370522 A370523 A370524 KEYWORD nonn AUTHOR Marius A. Burtea, Feb 27 2024 STATUS approved

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Last modified June 18 07:40 EDT 2024. Contains 373469 sequences. (Running on oeis4.)