A136734 -id:A136734 - cp's OEIS frontend

A141269 (0, 1, 2, 3, 2^2, 5, 23, 7, 2^3, 3^2, 25, 11, 2^2*3, ...) transform in (0+1, 2+3, 2+2, 5+2, 3+7, 2+3, 3+2, 2+5, 11+2, 2+3, ...).

1, 5, 4, 7, 10, 5, 5, 7, 13, 5, 15, 10, 7, 21, 5, 21, 4, 8, 9, 34, 5, 8, 4, 16, 5, 9, 31, 8, 33, 8, 13, 22, 9, 5, 39, 21, 16, 5, 46, 5, 50, 4, 14, 7, 25, 49, 7, 9, 7, 5, 19, 15, 55, 6, 16, 5, 10, 21, 88, 4, 8, 63, 34, 9, 8, 18, 5, 78, 4, 20, 25, 12, 73, 6, 75, 39, 8, 4, 21, 18, 5, 92, 6, 8, 6

Offset: 1

Juri-Stepan Gerasimov, Aug 08 2008

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Cf. A136734, A141270.

Corrected at three or more places by R. J. Mathar, Feb 21 2009

A141270 (0, 1, 2, 3, 2^2, 5, 23, 7, 2^3, 3^2, 25, 11, 2^23, ...) transform in (01, 23, 22, 52, 37, 23, 32, 25, 112, 2*3, ...).

Original entry on oeis.org

0, 6, 4, 10, 21, 6, 6, 10, 22, 6, 26, 21, 10, 68, 6, 38, 4, 15, 14, 253, 6, 15, 4, 39, 6, 14, 58, 15, 62, 15, 22, 85, 14, 6, 74, 38, 39, 6, 205, 6, 301, 4, 33, 10, 46, 94, 12, 14, 10, 6, 34, 26, 106, 9, 55, 6, 21, 38, 1711, 4, 15, 122, 93, 14, 12, 65, 6, 737, 4, 51, 46, 35, 142, 9

Offset: 1

Juri-Stepan Gerasimov, Aug 08 2008

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Cf. A136734, A141269.

Map[Times @@ # &, Partition[Flatten[{0}~Join~Array[DeleteCases[Flatten@ FactorInteger[#], 1] &, 72] /. {} -> {1}], 2, 2]] (* Michael De Vlieger, Oct 20 2021 *)

A 65 replaced with 85, a 54 with 74, etc. by R. J. Mathar, Feb 21 2009

A144190 (0, 1, 2, 3, 2^2, 5, 23, 7, 2^3, 3^2, 25, 11, 2^2*3, ...) becomes (0 mod 1, 2 mod 3, 2 mod 2, 5 mod 2, 3 mod 7, 2 mod 3, 3 mod 2, 2 mod 5, 11 mod 2, 2 mod 3, ...).

Original entry on oeis.org

0, 2, 0, 1, 3, 2, 1, 2, 1, 2, 1, 1, 1, 4, 2, 2, 0, 2, 1, 11, 2, 3, 0, 1, 1, 2, 1, 3, 1, 2, 1, 2, 1, 2, 2, 2, 3, 2, 5, 2, 7, 0, 2, 2, 2, 1, 1, 1, 2, 2, 1, 2, 1, 0, 5, 2, 1, 1, 29, 0, 3, 1, 1, 2, 2, 5, 2, 11, 0, 2, 1, 5, 1, 0, 2, 2, 3, 0, 2, 7, 2, 13, 2, 2, 0, 41, 0, 3, 5, 2, 3, 2, 11, 2, 2, 7, 0, 2, 1, 2, 1, 2, 1

Offset: 1

Juri-Stepan Gerasimov, Nov 20 2008

nonn

			2 mod 3 = 1 = a(10),
13 mod 2 = 1 = a(11),
7 mod 3 = 1 = a(12),
5 mod 2 = 1 = a(13),
4 mod 17 = 4 = a(14),
2 mod 3 = 2 = a(15),
2 mod 19 = 2 = a(16),
2 mod 2 = 0 = a(17),
5 mod 3 = 2 = a(18),
7 mod 2 = 1 = a(19),
11 mod 23 = 11 = a(20), etc.

Cf. A136734, A136735, A143653.

pflat := proc(nmax) local a, ifs, n, p, c ; a := [0,1] ; for n from 2 to nmax do ifs := ifactors(n)[2] ; for p in ifs do a := [op(a),op(1,p)] ; if op(2,p) > 1 then a := [op(a),op(2,p)] ; fi; od: od: a ; end: L := pflat(300) ; for n from 1 to nops(L)-2 by 2 do printf("%d,", op(n,L) mod op(n+1,L) ) ; end do: # R. J. Mathar, Apr 29 2010

a(10), a(43) and perhaps others corrected by R. J. Mathar, Apr 29 2010

cp's OEIS Frontend

A141269 (0, 1, 2, 3, 2^2, 5, 23, 7, 2^3, 3^2, 25, 11, 2^2*3, ...) transform in (0+1, 2+3, 2+2, 5+2, 3+7, 2+3, 3+2, 2+5, 11+2, 2+3, ...).

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A141270 (0, 1, 2, 3, 2^2, 5, 23, 7, 2^3, 3^2, 25, 11, 2^23, ...) transform in (01, 23, 22, 52, 37, 23, 32, 25, 112, 2*3, ...).

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A144190 (0, 1, 2, 3, 2^2, 5, 23, 7, 2^3, 3^2, 25, 11, 2^2*3, ...) becomes (0 mod 1, 2 mod 3, 2 mod 2, 5 mod 2, 3 mod 7, 2 mod 3, 3 mod 2, 2 mod 5, 11 mod 2, 2 mod 3, ...).

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cp's OEIS Frontend

A141269 (0, 1, 2, 3, 2^2, 5, 2*3, 7, 2^3, 3^2, 2*5, 11, 2^2*3, ...) transform in (0+1, 2+3, 2+2, 5+2, 3+7, 2+3, 3+2, 2+5, 11+2, 2+3, ...).

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A141270 (0, 1, 2, 3, 2^2, 5, 2*3, 7, 2^3, 3^2, 2*5, 11, 2^2*3, ...) transform in (0*1, 2*3, 2*2, 5*2, 3*7, 2*3, 3*2, 2*5, 11*2, 2*3, ...).

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A144190 (0, 1, 2, 3, 2^2, 5, 2*3, 7, 2^3, 3^2, 2*5, 11, 2^2*3, ...) becomes (0 mod 1, 2 mod 3, 2 mod 2, 5 mod 2, 3 mod 7, 2 mod 3, 3 mod 2, 2 mod 5, 11 mod 2, 2 mod 3, ...).

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Examples

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Maple

Extensions

A141269 (0, 1, 2, 3, 2^2, 5, 23, 7, 2^3, 3^2, 25, 11, 2^2*3, ...) transform in (0+1, 2+3, 2+2, 5+2, 3+7, 2+3, 3+2, 2+5, 11+2, 2+3, ...).

A141270 (0, 1, 2, 3, 2^2, 5, 23, 7, 2^3, 3^2, 25, 11, 2^23, ...) transform in (01, 23, 22, 52, 37, 23, 32, 25, 112, 2*3, ...).

A144190 (0, 1, 2, 3, 2^2, 5, 23, 7, 2^3, 3^2, 25, 11, 2^2*3, ...) becomes (0 mod 1, 2 mod 3, 2 mod 2, 5 mod 2, 3 mod 7, 2 mod 3, 3 mod 2, 2 mod 5, 11 mod 2, 2 mod 3, ...).