A140611 Consecutive N at which the prime running totals of prime factors in composites are found.

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

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: A188586 A084372 A353543 * A333846 A076957 A310585

Adjacent sequences: A140608 A140609 A140610 * A140612 A140613 A140614

Keyword

easy,nonn

Author

Enoch Haga, May 19 2008

Status

approved