A324538 -id:A324538 - cp's OEIS frontend

A324537 a(n) = A003557(k), where k = Product_{d|n, d>2} prime(A297167(d)).

1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 4, 1, 5, 3, 1, 1, 6, 1, 3, 5, 7, 1, 12, 1, 11, 1, 5, 1, 54, 1, 1, 7, 13, 5, 36, 1, 17, 11, 9, 1, 250, 1, 7, 9, 19, 1, 60, 1, 15, 13, 11, 1, 30, 7, 5, 17, 23, 1, 1620, 1, 29, 5, 1, 11, 686, 1, 13, 19, 375, 1, 540, 1, 31, 15, 17, 7, 2662, 1, 45, 1, 37, 1, 3500, 13, 41, 23, 7, 1, 2430, 11, 19, 29, 43, 17, 420, 1, 35, 7, 75, 1

Offset: 1

Antti Karttunen, Mar 07 2019

nonn

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

Cf. A000961 (positions of ones), A003557, A297167, A300827, A324191, A324193, A324202, A324538.

A061395(n) = if(1==n, 0, primepi(vecmax(factor(n)[, 1])));
A297167(n) = if(1==n, 0, (A061395(n) + (bigomega(n)-omega(n)) - 1));
A003557(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 2] = f[i, 2]-1); factorback(f); }; \\ From A003557
A324537(n) = { my(m=1); fordiv(n, d, if(d>2, m *= prime(A297167(d)))); A003557(m); };

A001222(a(n)) = A324191(n) - 1.

A332827 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = A003557(A332824(n)) for all other numbers, except f(1) = 0.

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, Feb 25 2020

nonn

For all i, j:

A305801(i) = A305801(j) => a(i) = a(j).

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

Cf. A000010, A003557, A019565, A305801, A332824, A332826.

Cf. also A324538.

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; };
A019565(n) = {my(j,v); factorback(Mat(vector(if(n, #n=vecextract(binary(n), "-1..1")), j, [prime(j), n[j]])~))}; \\ From A019565
A332824(n) = { my(m=1); fordiv(n,d,m *= A019565(eulerphi(d))); (m); };
A003557(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 2] = f[i, 2]-1); factorback(f); };
Aux332827(n) = if(1==n,0,A003557(A332824(n)));
v332827 = rgs_transform(vector(up_to,n,Aux332827(n)));
A332827(n) = v332827[n];

cp's OEIS Frontend

A324537 a(n) = A003557(k), where k = Product_{d|n, d>2} prime(A297167(d)).

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