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A141573 Prime powers of pairs of the infinite list generated by the flat list of the factorizations of all integers. 0
1, 9, 32, 8, 49, 4, 27, 32, 121, 8, 169, 343, 25, 4, 131072, 8, 1162261467, 4, 125, 49, 895430243255237372246531, 4, 8, 3125, 8192, 27, 9, 128, 841, 243, 961, 4, 4, 177147, 131072, 78125, 4, 27, 1369, 6859, 169, 4, 45474735088646411895751953125, 8 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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 powers 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..44.

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

CROSSREFS

Cf. A000040, A025475.

Sequence in context: A266710 A159279 A048547 * A075433 A018833 A130510

Adjacent sequences:  A141570 A141571 A141572 * A141574 A141575 A141576

KEYWORD

nonn,less

AUTHOR

Juri-Stepan Gerasimov, Aug 17 2008

EXTENSIONS

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

STATUS

approved

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Last modified July 5 07:06 EDT 2020. Contains 335460 sequences. (Running on oeis4.)