OFFSET
1,1
COMMENTS
All terms are of the form p^4 * q, with primes p < q.
a(3) = 13203 = 3^4 * 163 is the only term for which q = 2*p^4 + 1; for all other terms, q is either 2*p^4 - 1 (e.g., a(1) = 496 = 2^4 * 31) or (p^4 + 1)/2 (e.g., a(2) = 3321 = 3^4 * 41).
LINKS
Jon E. Schoenfield, Table of n, a(n) for n = 1..10000
EXAMPLE
Table showing the first 20 terms and their prime factorizations. Because of the different relationships between the prime factors p and q for different terms (see Comments), neither the values of p nor those of q are nondecreasing.
.
n a(n) = p^4 * q
-- -------------------------------------
1 496 = 2^4 * 31
2 3321 = 3^4 * 41
3 13203 = 3^4 * 163
4 195625 = 5^4 * 313
5 780625 = 5^4 * 1249
6 2883601 = 7^4 * 1201
7 11527201 = 7^4 * 4801
8 107186761 = 11^4 * 7321
9 407879641 = 13^4 * 14281
10 3487920481 = 17^4 * 41761
11 39155632561 = 23^4 * 139921
12 250123560121 = 29^4 * 353641
13 47622568443841 = 47^4 * 9759361
14 95853663421561 = 61^4 * 6922921
15 322876778328721 = 71^4 * 12705841
16 403230060146161 = 73^4 * 14199121
17 3034217580863041 = 79^4 * 77900161
18 6333850463213521 = 103^4 * 56275441
19 13292221046055841 = 113^4 * 81523681
20 25335401515201441 = 103^4 * 225101761
MATHEMATICA
t[n_] := n*(n + 1)/2; Select[t /@ Range[10^5], DivisorSigma[0, #] == 10 &] (* Amiram Eldar, Nov 26 2021 *)
PROG
(PARI) select(x->(numdiv(x)==10), vector(10^5, k, k*(k+1)/2)) \\ Michel Marcus, Nov 26 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Jon E. Schoenfield, Nov 25 2021
STATUS
approved