A141573 Prime powers of pairs of the infinite list generated by the flat list of the factorizations of all integers.

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

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: A159279 A048547 A351713 * 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