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
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
KEYWORD
nonn
AUTHOR
Amarnath Murthy, Apr 23 2004
EXTENSIONS
More terms from Franklin T. Adams-Watters, Apr 28 2006
STATUS
approved