login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A341528 a(n) = n * sigma(A003961(n)), where A003961 shifts the prime factorization of n one step towards larger primes, and sigma is the sum of the divisors of n. 19
1, 8, 18, 52, 40, 144, 84, 320, 279, 320, 154, 936, 234, 672, 720, 1936, 340, 2232, 456, 2080, 1512, 1232, 690, 5760, 1425, 1872, 4212, 4368, 928, 5760, 1178, 11648, 2772, 2720, 3360, 14508, 1554, 3648, 4212, 12800, 1804, 12096, 2064, 8008, 11160, 5520, 2538, 34848, 6517, 11400, 6120, 12168, 3180, 33696, 6160, 26880 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
FORMULA
Multiplicative with a(p^e) = (p^e) * (q^(e+1)-1)/(q-1) where q = nextPrime(p).
a(n) = n * A003973(n) = n * A000203(A003961(n)).
From Antti Karttunen, Mar 29 2021: (Start)
a(n) <= A341529(n).
a(n) = A341529(n) - A341512(n).
a(n) = A342662(A003961(n)).
(End)
Sum_{k=1..n} a(k) ~ c * n^3, where c = (1/3) * Product_{p prime} p^3/((p+1)*(p^2-nextprime(p))) = 2.26342530..., where nextprime is A151800. - Amiram Eldar, Dec 08 2022
MATHEMATICA
Array[#1 DivisorSigma[1, #2] & @@ {#, Times @@ Map[#1^#2 & @@ # &, FactorInteger[#] /. {p_, e_} /; e > 0 :> {Prime[PrimePi@ p + 1], e}] - Boole[# == 1]} &, 56] (* Michael De Vlieger, Feb 22 2021 *)
PROG
(PARI)
A003961(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); }; \\ From A003961
A003973(n) = sigma(A003961(n));
A341528(n) = (n*A003973(n));
CROSSREFS
Sequence in context: A335440 A066721 A079704 * A032795 A120543 A337836
KEYWORD
nonn,mult
AUTHOR
Antti Karttunen, Feb 16 2021
STATUS
approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 21 10:26 EST 2024. Contains 370228 sequences. (Running on oeis4.)