A141572 Products of pairs of the infinite list of primes generated by flattening the factorizations of the integers.

2, 6, 10, 6, 14, 4, 9, 10, 22, 6, 26, 21, 10, 4, 34, 6, 57, 4, 15, 14, 253, 4, 6, 25, 26, 9, 6, 14, 58, 15, 62, 4, 4, 33, 34, 35, 4, 9, 74, 57, 26, 4, 205, 6, 301, 4, 33, 15, 46, 94, 4, 6, 49, 10, 15, 34, 26, 106, 9, 15, 22, 4, 21, 38, 1711, 4, 15, 122, 93, 21, 4, 4, 4, 65, 6, 737, 4

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 products by pairing construction, all but the first term are in A001358.

Links

Ivan Neretin, Table of n, a(n) for n = 1..10000

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(120) : 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

ps = Flatten[Table[ConstantArray[#[[1]], #[[2]]] & /@ FactorInteger[n], {n, 68}]]; a = ps[[Range[l = Length[ps]/2]*2 - 1]]*ps[[Range[l]*2]] (* Ivan Neretin, May 29 2015 *)

Crossrefs

Cf. A000040.

Sequence in context: A004055 A077933 A144762 * A141257 A122882 A136700

Adjacent sequences: A141569 A141570 A141571 * A141573 A141574 A141575

Keyword

nonn,less

Author

Juri-Stepan Gerasimov, Aug 17 2008

Extensions

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

Status

approved