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 A048138 a(n) = number of m such that sum of proper divisors of m (A001065(m)) is n. 26
 0, 1, 1, 0, 2, 1, 2, 1, 1, 1, 1, 2, 2, 2, 2, 2, 1, 2, 2, 3, 2, 2, 1, 3, 1, 2, 1, 2, 1, 5, 2, 3, 1, 3, 1, 4, 1, 1, 3, 4, 2, 5, 2, 3, 2, 3, 1, 6, 2, 4, 0, 3, 2, 6, 1, 5, 1, 3, 1, 6, 2, 3, 3, 6, 1, 6, 1, 2, 1, 5, 1, 8, 3, 4, 3, 5, 1, 7, 1, 6, 1, 4, 1, 8, 1, 5, 0, 5, 2, 9, 2, 4, 1, 4, 0, 9, 1, 3, 2, 6, 1, 8, 2, 7, 4 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,5 COMMENTS The offset is 2 since there are infinitely many numbers (all the primes) for which A001065 = 1. The graph of this sequence, shifted by 1, looks similar to that of A061358, which counts Goldbach partitions of n. - T. D. Noe, Dec 05 2008 For n > 2, a(n) <= A000009(n) as all divisor lists must have distinct values. - Roderick MacPhee, Sep 13 2016 The smallest k > 0 such that there are exactly n numbers whose sum of proper divisors is k is A125601(n). - Bernard Schott, Mar 23 2023 LINKS T. D. Noe, Table of n, a(n) for n = 2..10000 Carl Pomerance, The first function and its iterates, pp. 125-138 in Connections in Discrete Mathematics, ed. S. Butler et al., Cambridge, 2018. FORMULA From Bernard Schott, Mar 23 2023: (Start) a(n) = 0 iff n is in A005114 (untouchable numbers). a(n) = 1 iff n is in A057709 ("hermit" numbers). a(n) = 2 iff n is in A057710. a(n) > 1 iff n is in A160133. (End) EXAMPLE a(6) = 2 since 6 is the sum of the proper divisors of 6 and 25. MAPLE with(numtheory): for n from 2 to 150 do count := 0: for m from 1 to n^2 do if sigma(m) - m = n then count := count+1 fi: od: printf(`%d, `, count): od: PROG (PARI) list(n)=my(v=vector(n-1), k); for(m=4, n^2, k=sigma(m)-m; if(k>1 & k<=n, v[k-1]++)); v \\ Charles R Greathouse IV, Apr 21 2011 CROSSREFS Cf. A001065, A064440, A125601, A238895, A238896 (records). Cf. A005114, A057709, A057710, A160133. Sequence in context: A269975 A308069 A161895 * A165022 A030338 A231148 Adjacent sequences: A048135 A048136 A048137 * A048139 A048140 A048141 KEYWORD easy,nonn AUTHOR Naohiro Nomoto EXTENSIONS More terms from James A. Sellers, Feb 19 2001 STATUS approved

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Last modified August 12 06:37 EDT 2024. Contains 375085 sequences. (Running on oeis4.)