cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A324580 a(n) = n * A276086(n).

Original entry on oeis.org

0, 2, 6, 18, 36, 90, 30, 70, 120, 270, 450, 990, 300, 650, 1050, 2250, 3600, 7650, 2250, 4750, 7500, 15750, 24750, 51750, 15000, 31250, 48750, 101250, 157500, 326250, 210, 434, 672, 1386, 2142, 4410, 1260, 2590, 3990, 8190, 12600, 25830, 7350, 15050, 23100, 47250, 72450, 148050, 42000, 85750, 131250, 267750, 409500
Offset: 0

Views

Author

Antti Karttunen, Mar 09 2019

Keywords

Links

Crossrefs

Cf. A002110, A276086, A324198, A324577, A324578, A324579, A324582.

Programs

  • PARI
    A276086(n) = { my(i=0,m=1,pr=1,nextpr); while((n>0),i=i+1; nextpr = prime(i)*pr; if((n%nextpr),m*=(prime(i)^((n%nextpr)/pr));n-=(n%nextpr));pr=nextpr); m; };
A324580(n) = n*A276086(n);

Formula

a(n) = n * A276086(n).
For n >= 0, a(A002110(n)) = A002110(1+n).

A324577 a(n) = A025487(n) * A324576(n) = A025487(n) * A276086(A025487(n)).

Original entry on oeis.org

2, 6, 36, 30, 120, 300, 3600, 15000, 210, 672, 1260, 42000, 2940, 28224, 88200, 164640, 288120, 4609920, 216090000, 21176820, 564715200, 2310, 11880, 18480, 4435200, 19404000, 66555720, 44370480000, 50820, 1306800, 2845920, 63748608, 5856903360, 328703760, 306790176000, 12298440, 7906140000, 645668100, 33746919360, 15874550866944
Offset: 1

Views

Author

Antti Karttunen, Mar 09 2019

Keywords

Comments

Note that A324198(A025487(n)) = gcd(A025487(n), A324576(n)) = 1 for all n, because each term of A025487 is a product of primorials.

Links

Crossrefs

Cf. A025487, A276086, A324198, A324576, A324579, A324580.
Cf. also A324582 (a subsequence).

Programs

  • PARI
    A276086(n) = { my(i=0,m=1,pr=1,nextpr); while((n>0),i=i+1; nextpr = prime(i)*pr; if((n%nextpr),m*=(prime(i)^((n%nextpr)/pr));n-=(n%nextpr));pr=nextpr); m; };
A324577(n) = A025487(n)*A276086(A025487(n));

Formula

a(n) = A025487(n) * A324576(n) = A025487(n) * A276086(A025487(n)).
a(n) = A324580(A025487(n)).

A324541 Numbers that occur in range of A324580.

Original entry on oeis.org

0, 2, 6, 18, 30, 36, 70, 90, 120, 210, 270, 300, 434, 450, 650, 672, 990, 1050, 1260, 1386, 2142, 2250, 2310, 2590, 2940, 3600, 3990, 4410, 4642, 4750, 5978, 6996, 7350, 7500, 7650, 8190, 9114, 11880, 12600, 14058, 15000, 15050, 15750, 16170, 18480, 18522, 21186, 23100, 23870, 24750, 25830, 28224, 30030, 30870, 31250, 32830, 35970, 37114, 42000
Offset: 0

Views

Author

Antti Karttunen, Mar 10 2019

Keywords

Comments

Indexing begins from 0 because the term a(0) = 0 is a special case.
Sequence A324580 sorted into ascending order, with duplicate occurrences removed. The first such duplicate is 2250 = A324580(15) = 150*15 = A324580(18) = 125*18. The next is 5402250 = A324580(105) = A276086(105)*105 = A324580(125) = A276086(125)*125.
Terms after zero are the positions of nonzero terms in A324539.

Links

Crossrefs

Cf. A324540 (complement).
Cf. A002110 (a subsequence), A276086, A324539, A324579, A324580.

Programs

  • PARI
    A276086(n) = { my(i=0,m=1,pr=1,nextpr); while((n>0),i=i+1; nextpr = prime(i)*pr; if((n%nextpr),m*=(prime(i)^((n%nextpr)/pr));n-=(n%nextpr));pr=nextpr); m; };
A324539(n) = sumdiv(n,d,(d==A276086(n/d)));
for(n=1,oo,if(A324539(n)>0, print1(n, ", "))); \\ Print terms after zero.
  • PARI
    \\ This program is better for computing many terms:
search_limit = 9699690;
A324580(n) = n*A276086(n);
A324541list(lim) = { my(s=Set([]),k); for(n=1,lim, k=A324580(n); if(k<=lim, s = setunion([k], s))); Vec(s); };
v324541 = A324541list(search_limit);
A324541(n) = if(!n,n,v324541[n]);

A324578 Numbers n for which n*A276086(n) is a term of A055932.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 27, 28, 30, 35, 36, 40, 42, 44, 45, 48, 50, 54, 56, 60, 66, 70, 72, 75, 77, 80, 81, 84, 88, 90, 96, 98, 99, 100, 105, 108, 110, 112, 120, 125, 126, 128, 132, 135, 140, 143, 144, 147, 150, 160, 162, 165, 168, 176, 180, 189, 192, 196, 198, 200, 210, 224, 231, 240, 245, 250, 252, 256
Offset: 1

Views

Author

Antti Karttunen, Mar 09 2019

Keywords

Links

Crossrefs

Cf. A002110, A055932, A276086, A324579 (a subsequence), A324580.

Programs

  • PARI
    A276086(n) = { my(i=0,m=1,pr=1,nextpr); while((n>0),i=i+1; nextpr = prime(i)*pr; if((n%nextpr),m*=(prime(i)^((n%nextpr)/pr));n-=(n%nextpr));pr=nextpr); m; };
A324580(n) = n*A276086(n);
isA055932(n) = if(1==n,1,my(f=factor(n)); (primepi(f[#f~,1]) == #f~));
isA324578(n) = isA055932(A324580(n));
Showing 1-4 of 4 results.

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