A349747 Multiply perfect numbers whose 5-adic valuation is larger than their 3-adic valuation.

459818240, 51001180160, 41254809330254618094796800000, 417557910137818162642396224651585493401600000, 21908279635853187912360370114977853341696000000, 4602427236053495643738729034543787648483328000000, 1470295051205988580219996701010375287153623040000000, 56532758277786216648694678091722223342645673984000000

Offset: 1

Author

Antti Karttunen, Nov 30 2021

Keywords

• nonn

Comments

Among the first 1600 multiperfect numbers, there is only one term x for which A007949(x) > A007814(x), and that is x = 6088728021160320, a 4-perfect number, while there are none for which A112765(x) > A007814(x). Only 1, 6, 120, 30240 (incidentally, the first four terms of A007539) seem to be in A025487.

The abundancy index (sigma(n)/n) of the 18 initial terms is: 3, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 6, 6, 7, 6, 8.

Examples

			459818240 = 2^8 * 5 * 7 * 19 * 37 * 73 is included because while it is a multiple of 5, it is not a multiple of 3.
41254809330254618094796800000 = 2^19 * 3^4 * 5^5 * 7^3 * 11^3 * 13 * 19 * 31^3 * 37 * 41 * 61 is included, because the exponent of 5 (which is 5), is larger than the exponent of 3, which is 4.
		

Links

• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A007539, A007691, A007814, A007949, A025487, A112765.

Programs

Mathematica

mp = Cases[Import["https://oeis.org/A007691/b007691.txt", "Table"], {, }][[;; , 2]]; Select[mp, IntegerExponent[#, 5] > IntegerExponent[#, 3] &] (* Amiram Eldar, Nov 30 2021 *)

Formula

{k in A007691 | A112765(k) > A007949(k)}.