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 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 Antti Karttunen, Table of n, a(n) for n = 1..8191 Index entries for sequences computed from indices in prime factorization. Index entries for sequences related to sigma(n). 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 Cf. A000203, A003961, A003973, A016754 (positions of the odd terms), A151800, A341512, A341526, A341527, A341529, A341530, A342661, A342662, A342673. Sequence in context: A335440 A066721 A079704 * A032795 A120543 A337836 Adjacent sequences: A341525 A341526 A341527 * A341529 A341530 A341531 KEYWORD nonn,mult AUTHOR Antti Karttunen, Feb 16 2021 STATUS approved

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