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A140611
Consecutive N at which the prime running totals of prime factors in composites are found.
2
4, 6, 10, 15, 16, 24, 26, 32, 42, 72, 78, 81, 102, 111, 124, 168, 172, 182, 196, 205, 209, 212, 240, 243, 276, 299, 301, 308, 320, 326, 345, 357, 361, 412, 425, 426, 427, 429, 455, 477, 490, 494, 526, 564, 591, 605, 610, 637, 638, 645, 664, 670, 672, 682, 684
OFFSET
1,1
LINKS
FORMULA
Compute prime factors (without multiplicity) of consecutive composite N. Maintain a running sum of these prime factors. Whenever the running total at N is prime, add to the sequence.
EXAMPLE
a(2)=6 because when N=6 the sum of composite prime factors is 7 and this total is prime (nonprime totals are not in this sequence). The prime factor (without multiplicity) of the first composite 4 is 2; the second composite is 6 with prime factors 3 and 2, so 2+2+3=7, the prime sum of prime factors at N=6.
MATHEMATICA
Module[{nn=700, cmps}, cmps=Select[Range[nn], CompositeQ]; Select[ Thread[ {cmps, Accumulate[Total[FactorInteger[#][[All, 1]]]&/@cmps]}], PrimeQ[ #[[2]]]&]][[All, 1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Apr 22 2020 *)
CROSSREFS
Cf. A140610.
Sequence in context: A353543 A388014 A388971 * A333846 A076957 A310585
KEYWORD
easy,nonn
AUTHOR
Enoch Haga, May 19 2008
STATUS
approved