A286449 -id:A286449 - cp's OEIS frontend

A286450 Restricted growth sequence computed for A252750.

1, 1, 2, 3, 4, 5, 6, 3, 2, 7, 8, 1, 9, 10, 11, 12, 7, 13, 14, 5, 15, 16, 17, 14, 18, 19, 20, 21, 22, 23, 24, 12, 25, 1, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 1, 5, 56, 31, 57, 58, 59, 7, 60, 61, 62, 17, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81

Offset: 1

Antti Karttunen, May 13 2017

nonn

Antti Karttunen, Table of n, a(n) for n = 1..10000

Cf. A252750, A286448, A286449.

rgs_transform(invec) = { my(occurrences = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(occurrences,invec[i]), my(pp = mapget(occurrences, invec[i])); outvec[i] = outvec[pp] , mapput(occurrences,invec[i],i); outvec[i] = u; u++ )); outvec; };
write_to_bfile(start_offset,vec,bfilename) = { for(n=1, length(vec), write(bfilename, (n+start_offset)-1, " ", vec[n])); }
A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ This function from Michel Marcus
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t }; \\ Modified from code of M. F. Hasler
A252750(n) = (A003961(A005940(n+1)) - (2 * A005940(n+1)));
write_to_bfile(1,rgs_transform(vector(10000,n,A252750(n))),"b286450.txt");

A293438 Product of deficiencies of proper divisors of n.

Original entry on oeis.org

1, 1, 1, 1, 1, 2, 1, 1, 2, 4, 1, 0, 1, 6, 8, 1, 1, 0, 1, 8, 12, 10, 1, 0, 4, 12, 10, 24, 1, 0, 1, 1, 20, 16, 24, 0, 1, 18, 24, -16, 1, 0, 1, 80, 240, 22, 1, 0, 6, 152, 32, 120, 1, 0, 40, 0, 36, 28, 1, 0, 1, 30, 600, 1, 48, 0, 1, 224, 44, 4224, 1, 0, 1, 36, 912, 288, 60, 0, 1, 160, 140, 40, 1, 0, 64, 42, 56, 320, 1, 0, 72, 440, 60, 46, 72

Offset: 1

Antti Karttunen, Dec 01 2017

sign

There are only 643 negative values in range 1 .. 16384.

			The proper divisors of 15 are 1, 3, 5. Their deficiencies (A033879) are 1, 2, 4. Thus a(15) = 1*2*4 = 8.
The proper divisors of 18 are 1, 2, 3, 6, 9. Their deficiencies are 1, 1, 2, 0, 5, thus a(18) = 1*1*2*0*5 = 0.
The proper divisors of 40 are 1, 2, 4, 5, 8, 10, 20. Their deficiencies are 1, 1, 1, 4, 1, 2, -2, thus a(40) = 1 * 1 * 1 * 4 * 1 * 2 * -2 = -16.

Antti Karttunen, Table of n, a(n) for n = 1..16384

Cf. A033879, A286449.

A033879(n) = ((2*n)-sigma(n));
A293438(n) = { my(m=1); fordiv(n,d,if(dA033879(d))); (m); };

a(n) = Product_{d|n, dA033879(d).

a(A000040(n)) = 1, a(A000079(n)) = 1.

A318309 Restricted growth sequence transform of A083254 (2*phi(n) - n).

Original entry on oeis.org

1, 2, 1, 2, 3, 4, 5, 2, 3, 4, 6, 7, 8, 4, 1, 2, 9, 10, 11, 7, 3, 4, 12, 13, 9, 4, 6, 7, 14, 15, 16, 2, 17, 4, 18, 19, 20, 4, 6, 13, 21, 22, 23, 7, 3, 4, 24, 25, 20, 26, 18, 7, 27, 22, 28, 13, 9, 4, 29, 30, 31, 4, 6, 2, 32, 33, 34, 7, 35, 36, 37, 38, 39, 4, 5, 7, 40, 41, 42, 25, 14, 4, 43, 44, 40, 4, 28, 13, 45, 46, 47, 7, 14, 4, 48, 49, 50, 15, 12, 51

Offset: 1

Antti Karttunen, Aug 26 2018

nonn

Antti Karttunen, Table of n, a(n) for n = 1..65537

Cf. A000010, A083254, A286449.

up_to = 65537;
rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om,invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om,invec[i],i); outvec[i] = u; u++ )); outvec; };
A083254(n) = (2*eulerphi(n)-n);
v318309 = rgs_transform(vector(up_to,n,A083254(n)));
A318309(n) = v318309[n];

A318308 Restricted growth sequence transform of A294898.

Original entry on oeis.org

1, 1, 1, 1, 2, 3, 4, 1, 4, 1, 5, 6, 7, 8, 2, 1, 9, 10, 11, 12, 5, 13, 14, 15, 16, 5, 17, 18, 19, 20, 21, 1, 16, 22, 23, 24, 25, 26, 14, 27, 28, 29, 30, 8, 31, 16, 32, 33, 30, 34, 35, 4, 36, 20, 25, 37, 38, 39, 40, 41, 42, 43, 16, 1, 44, 15, 45, 31, 46, 47, 48, 49, 50, 51, 39, 7, 52, 20, 53, 54, 30, 55, 56, 57, 58, 59, 60, 47, 61, 62, 63, 22, 40, 46, 64

Offset: 1

Antti Karttunen, Aug 26 2018

nonn

Antti Karttunen, Table of n, a(n) for n = 1..65537

Cf. A294898, A286449, A318309, A318310.

up_to = 65537;
rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om,invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om,invec[i],i); outvec[i] = u; u++ )); outvec; };
A294898(n) = (2*n - sigma(n) - hammingweight(n));
v318308 = rgs_transform(vector(up_to,n,A294898(n)));
A318308(n) = v318308[n];

cp's OEIS Frontend

A286450 Restricted growth sequence computed for A252750.

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A293438 Product of deficiencies of proper divisors of n.

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A318309 Restricted growth sequence transform of A083254 (2*phi(n) - n).

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A318308 Restricted growth sequence transform of A294898.

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