

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
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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 nonmembers of A005153 other than 10, 70 and 836?  Franklin T. AdamsWatters, 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[240], 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. AdamsWatters, Apr 28 2006


STATUS

approved



