

A141574


Sums of pairs of the infinite list generated by the flat list of the factorizations of all integers.


0



3, 5, 7, 5, 9, 4, 6, 7, 13, 5, 15, 10, 7, 4, 19, 5, 22, 4, 8, 9, 34, 4, 5, 10, 15, 6, 5, 9, 31, 8, 33, 4, 4, 14, 19, 12, 4, 6, 39, 22, 15, 4, 46, 5, 50, 4, 14, 8, 25, 49, 4, 5, 14, 7, 8, 19, 15, 55, 6, 8, 13, 4, 10, 21, 88, 4, 8, 63, 34, 10, 4, 4, 4, 18, 5, 78, 4, 20, 25, 12, 73, 4, 6, 75
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OFFSET

1,1


COMMENTS

Factorize n to its full extent into the list 1, 2, 3, 2*2, 5, 2*3, 7, 2*2*2, 3*3, 2*5, 11, 2*2*3,..
Remove delimiting commas and the multiplication signs and build new sums by pairing consecutive pairs of numbers of this list, 1+2, 3+2, 2+5, 2+3, 7+2, 2+2, 3+3, 2+5, 11+2, 2+3.. to construct the sequence.


LINKS

Table of n, a(n) for n=1..84.


MAPLE

pflat := proc(nmax) local a, ifs, n, p, c ; a := [1] ; for n from 2 to nmax do ifs := ifactors(n)[2] ; for p in ifs do q := op(1, p) ; for c from 1 to op(2, p) do a := [op(a), q] ; od: od: od: a ; end: pL := pflat(90) : for n from 1 to nops(pL)2 by 2 do printf("%d, ", op(n, pL)+op(n+1, pL)) ; od: # R. J. Mathar, Aug 21 2008


MATHEMATICA

f[n_] := Flatten[ Table[ First@#, {Last@#}] & /@ FactorInteger@n]; Plus @@@ Partition[ Flatten@ Array[f, 74], 2] (* Robert G. Wilson v, Aug 31 2008 *)


CROSSREFS

Cf. A000040.
Sequence in context: A070647 A070949 A222579 * A141261 A077129 A073409
Adjacent sequences: A141571 A141572 A141573 * A141575 A141576 A141577


KEYWORD

nonn,less


AUTHOR

JuriStepan Gerasimov, Aug 17 2008


EXTENSIONS

Edited, corrected and extended by R. J. Mathar, Aug 21 2008


STATUS

approved



