This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A322310 a(n) = Product_{d|n, d+1 is prime} A008578(1+[Sum_{i=0..A286561(n,1+d)} A320000((n/d)/((1+d)^i), 1+d)]). Here A286561(n,k) gives the k-valuation of n (for k > 1). 5
 3, 6, 1, 10, 1, 12, 1, 14, 1, 4, 1, 28, 1, 1, 1, 22, 1, 12, 1, 20, 1, 4, 1, 102, 1, 1, 1, 4, 1, 4, 1, 26, 1, 1, 1, 66, 1, 1, 1, 104, 1, 12, 1, 6, 1, 4, 1, 92, 1, 1, 1, 4, 1, 4, 1, 6, 1, 4, 1, 132, 1, 1, 1, 34, 1, 4, 1, 1, 1, 4, 1, 1240, 1, 1, 1, 1, 1, 4, 1, 57, 1, 4, 1, 21, 1, 1, 1, 28, 1, 1, 1, 6, 1, 1, 1, 492, 1, 1, 1, 12, 1, 4, 1, 6, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Antti Karttunen, Table of n, a(n) for n = 1..16384 FORMULA a(n) = Product_{d|n} A008578(1+[Sum_{i=0..A286561(n,1+d)} A320000((n/d)/((1+d)^i), 1+d)])^A010051(1+d). For all n, A056239(a(n)) = A014197(n). PROG (PARI) A320000sq(n, k) = if(1==n, if(1==k, 2, 1), sumdiv(n, d, if(d>=k && isprime(d+1), my(p=d+1, q=n/d); sum(i=0, valuation(n, p), A320000sq(q/(p^i), p))))); \\ From A320000 A322310(n) = if(1==n, 3, my(m=1); fordiv(n, d, my(s, p=d+1, q=n/d); if(isprime(p) && (s = sum(i=0, valuation(n, p), A320000sq(q/(p^i), p))), m *= prime(s))); (m)); CROSSREFS Cf. A014197, A320000, A322311 (rgs-transform). Cf. also A322312. Sequence in context: A108813 A108591 A110119 * A152202 A210039 A026250 Adjacent sequences:  A322307 A322308 A322309 * A322311 A322312 A322313 KEYWORD nonn AUTHOR Antti Karttunen, Dec 03 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.

Last modified December 7 22:29 EST 2019. Contains 329850 sequences. (Running on oeis4.)