A136735 -id:A136735 - cp's OEIS frontend

A143710 (1, 2, 3, 2^2, 5, 23, 7, 2^3, 3^2, 25, 11, 2^23, 13, 27, 3*5,..) becomes (1+2+3, 2+2+5, 2+3+7, 2+3+3, 2+2+5, 11+2+2, 3+13+2, 7+3+5,..).

6, 9, 12, 8, 9, 15, 18, 15, 23, 7, 23, 15, 36, 8, 9, 19, 11, 34, 38, 19, 24, 11, 42, 24, 18, 48, 53, 15, 10, 72, 9, 11, 10, 21, 68, 11, 16, 29, 90, 7, 68, 36, 15, 20, 81, 21, 28, 83, 8, 77, 45, 6, 37, 18, 85, 12, 126, 7, 29, 48, 34, 102, 10, 22, 28, 80, 26, 105, 11, 16, 9, 105, 123

Offset: 1

Juri-Stepan Gerasimov, Nov 13 2008

			a(8)=7+3+5=15.
a(9)=2+4+17=23.
a(10)=2+3+2=7.
a(11)=19+2+2=23.
a(12)=5+3+7=15.
a(13)=2+11+23=36,
etc.

Cf. A141287, A141261, A136735.

a(43) corrected by R. J. Mathar, Apr 14 2010

A143704 (1, 2, 3, 2^2, 5, 23, 7, 2^3, 3^2, 25, 11, 2^23, 13, 27, 35, ...) becomes ((1+2)3, (2+2)5, (2+3)7, (2+3)3, (2+2)5, (11+2)2, (3+13)2, (7+3)*5, ...).

Original entry on oeis.org

9, 20, 35, 15, 20, 26, 32, 50, 102, 10, 42, 56, 299, 15, 14, 48, 28, 93, 72, 88, 95, 18, 185, 63, 45, 92, 430, 44, 25, 1175, 18, 18, 21, 38, 132, 30, 39, 190, 1829, 12, 132, 68, 54, 36, 938, 68, 52, 852, 15, 150, 200, 8, 286, 65, 324, 32, 3569, 12, 204, 135, 93, 200, 25, 40

Offset: 1

Juri-Stepan Gerasimov, Nov 13 2008

nonn

			a(8)  = ( 7 +  3) *  5 = 10*5 = 50;
a(9)  = ( 2 +  4) * 17 = 102;
a(10) = ( 2 +  3) *  2 =  10;
a(11) = (19 +  2) *  2 =  42;
a(12) = ( 5 +  3) *  7 =  56;
a(13) = ( 2 + 11) * 23 = 199;
etc.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A141287, A141261, A136735.

g:= proc(n) local L; L:= sort(ifactors(n)[2],(s,t) -> s[1]Robert Israel, Nov 16 2019

Corrected (199 replaced by 299, 60 replaced by 30, 549 replaced by 54 etc.) by R. J. Mathar, Apr 18 2010

A143711 (1, 2, 3, 2^2, 5, 23, 7, 2^3, 3^2, 25, 11, 2^23, 13, 27, 35,..) becomes (12*3, 225, 237, 233, 225, 1122, 3132, 735,..).

Original entry on oeis.org

6, 20, 42, 18, 20, 44, 78, 105, 136, 12, 76, 105, 506, 18, 20, 117, 28, 174, 310, 165, 170, 28, 222, 114, 78, 410, 903, 44, 30, 2162, 24, 28, 30, 68, 1378, 45, 66, 399, 3422, 12, 610, 186, 84, 130, 2211, 68, 138, 2485, 18, 292, 555, 8, 1463, 78, 632, 60, 6806, 12

Offset: 1

Juri-Stepan Gerasimov, Nov 13 2008

nonn

			a(8)=7*3*5=105.
a(9)=2*4*17=136.
a(10)=2*3*2=12.
a(11)=19*2*2=76.
a(12)=5*3*7=105.
a(13)=2*11*23=506,
etc.

Cf. A141287, A141261, A136735.

a(43) corrected by R. J. Mathar, Apr 14 2010

A143705 (1, 2, 3, 2^2, 5, 23, 7, 2^3, 3^2, 25, 11, 2^23, 13, 27, 3*5,..) becomes ((1+2)^3, (2+2)^5, (2+3)^7, (2+3)^3, (2+2)^5, (11+2)^2, (3+13)^2, (7+3)^5,..).

Original entry on oeis.org

27, 1024, 78125, 125, 1024, 169, 256, 100000, 16926659444736, 25, 441, 2097152, 41753905413413116367045797, 125, 49, 4096, 16384, 29791, 1296, 8589934592, 2476099, 81, 72759576141834259033203125, 9261, 3375

Offset: 1

Juri-Stepan Gerasimov, Nov 13 2008

nonn

			a(8)=(7+3)^5=10^5=100000.
a(9)=(2+4)^17=6^17=16926659444736..
a(10)=(2+3)^2=5^2=25.
a(11)=(19+2)^2=21^2=441.
a(12)=(5+3)^7=8^7=2097152,
etc.

Cf. A141287, A141261, A136735.

Corrected (161051 removed) and extended by R. J. Mathar, Apr 18 2010

A143706 (1, 2, 3, 2^2, 5, 23, 7, 2^3, 3^2, 25, 11, 2^23, 13, 27, 35,..) becomes (12+3, 22+5, 23+7, 23+3, 22+5, 112+2, 313+2, 7*3+5,..).

Original entry on oeis.org

5, 9, 13, 9, 9, 24, 41, 26, 25, 8, 40, 22, 45, 9, 12, 42, 11, 61, 157, 26, 39, 16, 43, 41, 29, 207, 64, 15, 11, 93, 11, 16, 13, 36, 691, 14, 25, 40, 117, 7, 307, 95, 20, 67, 100, 21, 71, 106, 9, 148, 116, 6, 144, 19, 162, 19, 165, 7, 52, 89, 61, 981, 11, 93, 49, 109, 97, 112

Offset: 1

Juri-Stepan Gerasimov, Nov 13 2008

nonn

			a(8)=7*3+5=21+5=26.
a(9)=2*4+17=8+17=25.
a(10)=2*3+2=6+2=8.
a(11)=19*2+2=38+2=40.
a(12)=5*3+7=15+7=22.
a(13)=2*11+23=22+23=45,
etc.

Cf. A141287, A141261, A136735.

Corrected (9 duplicated, 75 replaced by 20 etc.) by R. J. Mathar, Apr 18 2010

A143707 (1, 2, 3, 2^2, 5, 23, 7, 2^3, 3^2, 25, 11, 2^23, 13, 27, 35,..) becomes (1(2+3), 2(2+5), 2(3+7), 2(3+3), 2(2+5), 11(2+2), 3(13+2), 7*(3+5),..).

Original entry on oeis.org

5, 14, 20, 12, 14, 44, 45, 56, 42, 10, 76, 50, 68, 12, 20, 78, 18, 145, 165, 70, 44, 28, 117, 44, 65, 215, 150, 26, 21, 140, 14, 28, 25, 68, 715, 24, 55, 154, 176, 10, 315, 155, 56, 75, 234, 38, 75, 390, 12, 150, 296, 8, 342, 32, 474, 35, 248, 10, 154, 92, 145, 1001, 21, 105

Offset: 1

Juri-Stepan Gerasimov, Nov 13 2008

nonn

			a(8)=7*(3+5)=7*8=56.
a(9)=2*(4+17)=2*21=42.
a(10)=2*(3+2)=2*5=10.
a(11)=19*(2+2)=19*4=40.
a(12)=5*(3+7)=5*10=50.
a(13)=2*(11+23)=2*34=68,
etc.

Cf. A141287, A141261, A136735.

Corrected (40 replaced by 76, 18 by 12, 90 by 70 etc.) by R. J. Mathar, Apr 18 2010

A143708 (1, 2, 3, 2^2, 5, 23, 7, 2^3, 3^2, 25, 11, 2^23, 13, 27, 3*5,..) becomes (1^(2+3), 2^(2+5), 2^(3+7), 2^(3+3), 2^(2+5), 11^(2+2), 3^(13+2), 7^(3+5),..).

Original entry on oeis.org

1, 128, 1024, 64, 128, 14641, 14348907, 5764801, 2097152, 32, 130321, 9765625, 17179869184, 64, 625, 4826809, 512, 20511149, 116415321826934814453125, 6103515625, 4194304, 2401, 4052555153018976267, 4194304, 371293

Offset: 1

Juri-Stepan Gerasimov, Nov 13 2008

nonn

			a(8)=7^(3+5)=7^8=5764801.
a(9)=2^(4+17)=2^21=2097152.
a(10)=2^(3+2)=2^5=32.
a(11)=19^(2+2)=19^4=130321.
a(12)=5^(3+7)=5^10=9765625.
a(13)=2^(11+23)=2^34=17179869184,
etc.

Cf. A141287, A141261, A136735.

More terms from R. J. Mathar, Apr 18 2010

A143709 (1, 2, 3, 2^2, 5, 23, 7, 2^3, 3^2, 25, 11, 2^23, 13, 27, 3*5,..) becomes (1^2+3, 2^2+5, 2^3+7, 2^3+3, 2^2+5, 11^2+2, 3^13+2, 7^3+5,..).

Original entry on oeis.org

4, 9, 15, 11, 9, 123, 1594325, 348, 33, 10, 363, 132, 2071, 11, 27, 2200, 11, 844, 4656612873077392578127, 136, 131077, 51, 46, 524291, 172, 45474735088646411895751953127, 2230, 15, 14, 8388655, 19, 51, 28, 291

Offset: 1

Juri-Stepan Gerasimov, Nov 13 2008

nonn

			a(8)=7^3+5=343+5=348.
a(9)=2^4+17=16+17=43.
a(10)=2^3+2=8+2=10.
a(11)=19^2+2=361+2=363.
a(12)=5^3+7=125+7=132.
a(13)=2^11+23=2048+23=2071,
etc.

Cf. A141287, A141261, A136735.

Corrected (15 replaced by 9, 43 by 33) and extended by R. J. Mathar, Apr 18 2010

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

A143710 (1, 2, 3, 2^2, 5, 2*3, 7, 2^3, 3^2, 2*5, 11, 2^2*3, 13, 2*7, 3*5,..) becomes (1+2+3, 2+2+5, 2+3+7, 2+3+3, 2+2+5, 11+2+2, 3+13+2, 7+3+5,..).

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A143704 (1, 2, 3, 2^2, 5, 2*3, 7, 2^3, 3^2, 2*5, 11, 2^2*3, 13, 2*7, 3*5, ...) becomes ((1+2)*3, (2+2)*5, (2+3)*7, (2+3)*3, (2+2)*5, (11+2)*2, (3+13)*2, (7+3)*5, ...).

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A143711 (1, 2, 3, 2^2, 5, 2*3, 7, 2^3, 3^2, 2*5, 11, 2^2*3, 13, 2*7, 3*5,..) becomes (1*2*3, 2*2*5, 2*3*7, 2*3*3, 2*2*5, 11*2*2, 3*13*2, 7*3*5,..).

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A143705 (1, 2, 3, 2^2, 5, 2*3, 7, 2^3, 3^2, 2*5, 11, 2^2*3, 13, 2*7, 3*5,..) becomes ((1+2)^3, (2+2)^5, (2+3)^7, (2+3)^3, (2+2)^5, (11+2)^2, (3+13)^2, (7+3)^5,..).

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A143706 (1, 2, 3, 2^2, 5, 2*3, 7, 2^3, 3^2, 2*5, 11, 2^2*3, 13, 2*7, 3*5,..) becomes (1*2+3, 2*2+5, 2*3+7, 2*3+3, 2*2+5, 11*2+2, 3*13+2, 7*3+5,..).

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A143707 (1, 2, 3, 2^2, 5, 2*3, 7, 2^3, 3^2, 2*5, 11, 2^2*3, 13, 2*7, 3*5,..) becomes (1*(2+3), 2*(2+5), 2*(3+7), 2*(3+3), 2*(2+5), 11*(2+2), 3*(13+2), 7*(3+5),..).

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A143708 (1, 2, 3, 2^2, 5, 2*3, 7, 2^3, 3^2, 2*5, 11, 2^2*3, 13, 2*7, 3*5,..) becomes (1^(2+3), 2^(2+5), 2^(3+7), 2^(3+3), 2^(2+5), 11^(2+2), 3^(13+2), 7^(3+5),..).

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A143709 (1, 2, 3, 2^2, 5, 2*3, 7, 2^3, 3^2, 2*5, 11, 2^2*3, 13, 2*7, 3*5,..) becomes (1^2+3, 2^2+5, 2^3+7, 2^3+3, 2^2+5, 11^2+2, 3^13+2, 7^3+5,..).

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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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A143710 (1, 2, 3, 2^2, 5, 23, 7, 2^3, 3^2, 25, 11, 2^23, 13, 27, 3*5,..) becomes (1+2+3, 2+2+5, 2+3+7, 2+3+3, 2+2+5, 11+2+2, 3+13+2, 7+3+5,..).

A143704 (1, 2, 3, 2^2, 5, 23, 7, 2^3, 3^2, 25, 11, 2^23, 13, 27, 35, ...) becomes ((1+2)3, (2+2)5, (2+3)7, (2+3)3, (2+2)5, (11+2)2, (3+13)2, (7+3)*5, ...).

A143711 (1, 2, 3, 2^2, 5, 23, 7, 2^3, 3^2, 25, 11, 2^23, 13, 27, 35,..) becomes (12*3, 225, 237, 233, 225, 1122, 3132, 735,..).

A143705 (1, 2, 3, 2^2, 5, 23, 7, 2^3, 3^2, 25, 11, 2^23, 13, 27, 3*5,..) becomes ((1+2)^3, (2+2)^5, (2+3)^7, (2+3)^3, (2+2)^5, (11+2)^2, (3+13)^2, (7+3)^5,..).

A143706 (1, 2, 3, 2^2, 5, 23, 7, 2^3, 3^2, 25, 11, 2^23, 13, 27, 35,..) becomes (12+3, 22+5, 23+7, 23+3, 22+5, 112+2, 313+2, 7*3+5,..).

A143707 (1, 2, 3, 2^2, 5, 23, 7, 2^3, 3^2, 25, 11, 2^23, 13, 27, 35,..) becomes (1(2+3), 2(2+5), 2(3+7), 2(3+3), 2(2+5), 11(2+2), 3(13+2), 7*(3+5),..).

A143708 (1, 2, 3, 2^2, 5, 23, 7, 2^3, 3^2, 25, 11, 2^23, 13, 27, 3*5,..) becomes (1^(2+3), 2^(2+5), 2^(3+7), 2^(3+3), 2^(2+5), 11^(2+2), 3^(13+2), 7^(3+5),..).

A143709 (1, 2, 3, 2^2, 5, 23, 7, 2^3, 3^2, 25, 11, 2^23, 13, 27, 3*5,..) becomes (1^2+3, 2^2+5, 2^3+7, 2^3+3, 2^2+5, 11^2+2, 3^13+2, 7^3+5,..).

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, ...).