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 A093891 Numbers k such that every prime up to sigma(k) is a sum of divisors of k. 6
 1, 2, 4, 6, 8, 10, 12, 16, 18, 20, 24, 28, 30, 32, 36, 40, 42, 48, 54, 56, 60, 64, 66, 70, 72, 78, 80, 84, 88, 90, 96, 100, 104, 108, 112, 120, 126, 128, 132, 140, 144, 150, 156, 160, 162, 168, 176, 180, 192, 196, 198, 200, 204, 208, 210, 216, 220, 224, 228, 234, 240 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Sequence is infinite as sigma (2^n) = 2^(n+1)-1 and a(2^n) = pi(2^(n+1)-1). Does this sequence include any non-members of A005153 other than 10, 70 and 836? - Franklin T. Adams-Watters, Apr 28 2006 The answer to the previous comment is yes, this sequence has many terms that are not in A005153. See A174434. - T. D. Noe, Mar 19 2010 LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 EXAMPLE 4 is a member as sigma(4) = 7 and all the primes up to 7 are a partial sum of divisors of 4, since divisors of 4 are 1, 2 and 4 and because primes arising are 2, 3 = 1+2, 5 = 1+4 and 7 = 1+2+4. MATHEMATICA Select[Range, SubsetQ[Total /@ Rest@ Subsets@ Divisors[#], Prime@ Range@ PrimePi@ DivisorSigma[1, #]] &] (* Michael De Vlieger, Mar 19 2021 *) PROG (PARI) isok(m) = {my(d=divisors(m), vp = primes(primepi(sigma(m)))); for (i=1, 2^#d - 1, my(b = Vecrev(binary(i)), x = sum(k=1, #b, b[k]*d[k])); if (vecsearch(vp, x), vp = setminus(vp, Set(x))); if (#vp == 0, return (1)); ); } \\ Michel Marcus, Mar 19 2021 CROSSREFS Cf. A093890, A093892. Cf. A005153. Sequence in context: A114871 A085150 A051178 * A213708 A239063 A151999 Adjacent sequences:  A093888 A093889 A093890 * A093892 A093893 A093894 KEYWORD nonn AUTHOR Amarnath Murthy, Apr 23 2004 EXTENSIONS More terms from Franklin T. Adams-Watters, Apr 28 2006 STATUS approved

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Last modified May 6 17:59 EDT 2021. Contains 343586 sequences. (Running on oeis4.)