A319345 -id:A319345 - cp's OEIS frontend

A318881 Restricted growth sequence transform of A277906, the least number with same prime signature as phi(n).

1, 1, 2, 2, 3, 2, 4, 3, 4, 3, 4, 3, 5, 4, 6, 6, 7, 4, 5, 6, 5, 4, 4, 6, 5, 5, 5, 5, 5, 6, 8, 7, 5, 7, 9, 5, 10, 5, 9, 7, 9, 5, 8, 5, 9, 4, 4, 7, 8, 5, 11, 9, 5, 5, 9, 9, 10, 5, 4, 7, 12, 8, 10, 11, 13, 5, 8, 11, 5, 9, 8, 9, 14, 10, 9, 10, 12, 9, 8, 11, 9, 9, 4, 9, 15, 8, 9, 9, 9, 9, 14, 5, 12, 4, 14, 11, 16, 8, 12, 9, 10, 11, 8, 13, 13

Offset: 1

Antti Karttunen, Sep 17 2018

nonn

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

Cf. A000010, A046523, A277906, A319342, A319343, A319344, A319345.

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; };
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
A277906(n) = A046523(eulerphi(n));
v318881 = rgs_transform(vector(up_to,n,A277906(n)));
A318881(n) = v318881[n];

A319343 Filter sequence combining the prime signature of phi(d) from all proper divisors d of n.

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, Sep 17 2018

nonn

Restricted growth sequence transform of A319342.

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

Cf. A318881, A319342, A319345.

Cf. also A305983.

up_to = 65537;
A319342(n) = { my(m=1); fordiv(n, d, if((dA318881(d)))); (m); }; \\ Needs also code from A318881
v319343 = rgs_transform(vector(up_to,n,A319342(n)));
A319343(n) = v319343[n];

A319344 a(n) = Product_{d|n, d>1} prime(A318881(d)), where A318881(d) records the prime signature of A000010(d).

Original entry on oeis.org

1, 2, 3, 6, 5, 18, 7, 30, 21, 50, 7, 270, 11, 98, 195, 390, 17, 882, 11, 1950, 231, 98, 7, 17550, 55, 242, 231, 3234, 11, 76050, 19, 6630, 231, 578, 805, 145530, 29, 242, 759, 165750, 23, 106722, 19, 3234, 31395, 98, 7, 3878550, 133, 6050, 1581, 16698, 11, 106722, 805, 371910, 957, 242, 7, 252105750, 37, 722, 46893, 205530, 2255, 106722, 19

Offset: 1

Antti Karttunen, Sep 17 2018

nonn

Antti Karttunen, Table of n, a(n) for n = 1..8192

Cf. A318881, A319342, A319345 (rgs-transform).

Cf. also A305984.

A319344(n) = { my(m=1); fordiv(n, d, if((d>1), m *= prime(A318881(d)))); (m); }; \\ Needs also code from A318881

a(n) = Product_{d|n, d>1} prime(A318881(d)).

cp's OEIS Frontend

A318881 Restricted growth sequence transform of A277906, the least number with same prime signature as phi(n).

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A319343 Filter sequence combining the prime signature of phi(d) from all proper divisors d of n.

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A319344 a(n) = Product_{d|n, d>1} prime(A318881(d)), where A318881(d) records the prime signature of A000010(d).

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