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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

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: A188592 A188586 A084372 * A333846 A076957 A310585

Adjacent sequences:  A140608 A140609 A140610 * A140612 A140613 A140614

KEYWORD

easy,nonn

AUTHOR

Enoch Haga, May 19 2008

STATUS

approved

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Last modified April 13 20:46 EDT 2021. Contains 342941 sequences. (Running on oeis4.)