A141574 Sums of pairs of the infinite list generated by the flat list of the factorizations of all integers.

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

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

Juri-Stepan Gerasimov, Aug 17 2008

Extensions

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

Status

approved