login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A300841 Fermi-Dirac factorization prime shift towards larger terms: a(n) = A052330(2*A052331(n)). 12
1, 3, 4, 5, 7, 12, 9, 15, 11, 21, 13, 20, 16, 27, 28, 17, 19, 33, 23, 35, 36, 39, 25, 60, 29, 48, 44, 45, 31, 84, 37, 51, 52, 57, 63, 55, 41, 69, 64, 105, 43, 108, 47, 65, 77, 75, 49, 68, 53, 87, 76, 80, 59, 132, 91, 135, 92, 93, 61, 140, 67, 111, 99, 85, 112, 156, 71, 95, 100, 189, 73, 165, 79, 123, 116, 115, 117, 192, 81 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

With n having a unique factorization as A050376(i) * A050376(j) * ... * A050376(k), with i, j, ..., k all distinct, a(n) = A050376(1+i) * A050376(1+j) * ... * A050376(1+k).

Multiplicative because for coprime m and n the Fermi-Dirac factorizations of m and n are disjoint and their union is the Fermi-Dirac factorization of m * n. - Andrew Howroyd, Aug 02 2018

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..32768

FORMULA

a(n) = A052330(2*A052331(n)).

For all n >= 1, a(A050376(n)) = A050376(1+n).

For all n >= 1, A300840(a(n)) = n.

a(A059897(n,k)) = A059897(a(n), a(k)). - Peter Munn, Nov 23 2019

EXAMPLE

For n = 6 = A050376(1)*A050376(2), a(6) = A050376(2)*A050376(3) = 3*4 = 12.

For n = 12 = A050376(2)*A050376(3), a(12) = A050376(3)*A050376(4) = 4*5 = 20.

PROG

(PARI)

up_to_e = 8192;

v050376 = vector(up_to_e);

A050376(n) = v050376[n];

ispow2(n) = (n && !bitand(n, n-1));

i = 0; for(n=1, oo, if(ispow2(isprimepower(n)), i++; v050376[i] = n); if(i == up_to_e, break));

A052330(n) = { my(p=1, i=1); while(n>0, if(n%2, p *= A050376(i)); i++; n >>= 1); (p); };

A052331(n) = { my(s=0, e); while(n > 1, fordiv(n, d, if(((n/d)>1)&&ispow2(isprimepower(n/d)), e = vecsearch(v050376, n/d); if(!e, print("v050376 too short!"); return(1/0)); s += 2^(e-1); n = d; break))); (s); };

A300841(n) = A052330(2*A052331(n));

CROSSREFS

Cf. A050376, A052330, A052331, A059897, A300840 (a left inverse).

Cf. also A003961.

Range of values is A003159.

Sequence in context: A285224 A322991 A120635 * A023713 A032890 A092859

Adjacent sequences:  A300838 A300839 A300840 * A300842 A300843 A300844

KEYWORD

nonn,mult

AUTHOR

Antti Karttunen, Apr 12 2018

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 1 22:24 EST 2020. Contains 338858 sequences. (Running on oeis4.)